# data[].attributes.body
Most of the links are mentioned with the article itself. Slides having no link are mostly self written

# data[].attributes.body
I collected data using internet. E-books,youtube videos and tutorials and Powerpoint presentations from slideshare helped in understanding the topic faster.

# data[].attributes.headline
Application - How does the stock market affect the economy?

# data[].attributes.subject
Application - How does the stock market affect the economy?

# data[].attributes.body
Movements in the stock market can have a profound economic impact on the economy and everyday people. A collapse in share prices has the potential to cause widespread economic disruption. Most famously, the stock market crash of 1929 was a key factor in causing the great depression of the 1930s. Yet, daily movements in the stock market can also have less impact on the economy than we might imagine. During the great recession of 2009-13, the stock market performed quite strongly. This rise in share prices was rather misleading to the state of the economy. Also, a fall in share prices doesn’t necessarily cause an economic downturn.

For example, the stock market crash of 1987, didn’t cause any lasting economic damage. (though it did influence monetary policy. UK cut interest rates in fear the stock market crash would cause a recession. Instead, low interest rates caused a boom.

Plummeting share prices can make headline news. But, how much should we worry when share prices fall? How does it impact on the average consumer? and how does it affect the economy?

# data[].attributes.headline
References - Mathematics of Financial Markets

# data[].attributes.subject
References - Mathematics of Financial Markets

# data[].attributes.body
Journal by Mark Devis Published On 3 Sep 2000

1. L. Bachelier: Th´eorie de la Sp´eculation. Ann. Sci. Ecole Norm. Sup. 17 (1900) 21– 86 [English translation in P. Cootner (ed.) The Random Character of Stock Prices. MIT Press, 1964, reprinted Risk Books, London 2000] 2. P. L. Bernstein: Capital Ideas. The Free Press, New York 1992 3. F. Black and M. Scholes: The pricing of options and corporate liabilities. J. Political Econom. 81 (1973) 637–654 4. J. Cox, S. Ross and M. Rubinstein: Option pricing, a simplified approach. J. Financial Economics 7 (1979) 229–263 5. R. C. Dalang, A. Morton andW.Willinger: Equivalent martingale measures and noarbitrage in stochastic securities market models, Stochastics and Stochastics Reports 29 (1989) 185–202 6. M. H. A. Davis: Option pricing in incomplete markets, in M. A. H. Dempster and S. R. Pliska (eds.) Mathematics of Derivative Securities. Cambridge University Press 1997 7. F. Delbaen and W. Schachermayer: A general version of the fundamental theorem of asset pricing. Math. Ann. 300 (1994) 463–520 8. F. Delbaen and W. Schachermayer: The fundamental theorem of asset pricing for unbounded stochastic processes. Math. Ann. 312 (1998) 215–250 9. J. L. Doob: Stochastic Processes. Wiley, New York 1953 10. A. Einstein: U¨ ber die von der molekularkinetischen Theorie der Wa¨rme geforderte Bewegung von in ruhenden Fl¨ussigkeiten suspendierten Teilchen. Annalen der Physik 17 (1905) 549–560

# data[].attributes.headline
References-  Prediction of Stock Price Movement Using Continuous Time Models

# data[].attributes.subject
References-  Prediction of Stock Price Movement Using Continuous Time Models

# data[].attributes.body
Journal by Masimba E. Sonono,Hopolang P. Mashel Published On 22 May 2015

[1] Leung, M., Daouk, H. and Chen, A. (2000) Forecasting Stock Indices: A Comparison of Classification and Level Estimation Models. International Journal of Forecasting, 16, 173-190. http://dx.doi.org/10.1016/S0169-2070(99)00048-5 [2] Maberly, E.D. (1986) The Informational Content of the Interday Price Change with Respect to Stock Index. Journal of M. E. Sonono, H. P. Mashele 191 Futures Markets, 6, 385-395. http://dx.doi.org/10.1002/fut.3990060304 [3] Wu, Y. and Zhang, H. (1997) Forward Premiums as Unbiased Predictors of Future Currency Depreciation: A NonParametric Analysis. Journal of International Money and Finance, 16, 609-623. http://dx.doi.org/10.1016/S0261-5606(97)00022-3

[4] Aggarwal, R. and Demaskey, A. (1997) Using Derivatives in Major Currencies for Cross-Hedging Currency Risks in Asian Emerging Markets. Journal of Future Markets, 17, 781-796.
http://dx.doi.org/10.1002/(SICI)1096-9934(199710)17:7<781::AID-FUT3>3.0.CO;2-J [5] Imandoust, S. and Bolandraftar, M. (2014) Forecasting the Direction of Stock Market Index Movement Using Three Data Mining Techniques: The Case of Tehran Stock Exchange. International Journal of Engineering Research and Applications, 4, 106-117. [6] Abidin, S. and Jaffar, M.M. (2012) A Review on Geometric Brownian Motion in Forecasting the Share Prices in Bursa Malaysia. World Applied Sciences Journal, 17, 87-93. [7] Abidin, S. and Jaffar, M.M. (2014) Forecasting Share Prices of Small Size Companies in Bursa Malaysia. Applied Mathematics and Information Sciences, 8, 107-112. http://dx.doi.org/10.12785/amis/080112 [8] Mandelbrot, B.B. (1963) TheVariation of Speculative Prices. Journal of Business, 36, 394-419. http://dx.doi.org/10.1086/294632 [9] Fama, E. (1965) The Behaviour of Stock Market Prices. Journal of Business, 64, 34-105. http://dx.doi.org/10.1086/294632 [10] Madan, D.B. and Seneta, E. (1990) The Variance Gamma Model for Share Market Returns. Journal of Business, 64, 511-524. http://dx.doi.org/10.1086/296519

# data[].attributes.headline
Application -  Predicting crashes in financial markets
with the Log-Periodic Power Law

# data[].attributes.subject
Application -  Predicting crashes in financial markets
with the Log-Periodic Power Law

# data[].attributes.body
Speculative bubbles seen in financial markets, show similarities in the way they evolve and grow. This particular oscillating movement can be captured by an equation called Log-Periodic Power Law. The ending crash of a speculative bubble is the climax of this Log-Periodic oscillation. The most probable time of a crash is given by a parameter in the equation. By fitting the Log-Periodic Power Law equation to a financial time series, it is possible to predict the event of a crash. With a hybrid Genetic Algorithm it is possible to estimate the parameters in the equation. Until now, the methodology of performing these predictions has been vague. The ambition is to investigate if the financial crisis of 2008, which rapidly spread through the world, could have been predicted by the Log-Periodic Power Law. Analysis of the SP500 and the DJIA showed the signs of the Log-Periodic Power Law prior to the financial crisis of 2008. Even though the analyzed indices started to decline slowly at first and the severe drops came much further, the equation could predict a turning point of the downtrend. The opposite of a speculative bubble is called an anti-bubble, moving as a speculative bubble, but with a negative slope. This log-periodic oscillation has been detected in most of the speculative bubbles that ended in a crash during the Twentieth century and also for some antibubbles, that have been discovered. Is it possible to predict the course of the downtrend during the financial crisis of 2008, by applying this equation? The equation has been applied to the Swedish OMXS30 index, during the current financial crisis of 2008, with the result of a predicted course of the index.

# data[].attributes.headline
JournalAn Introduction to Financial Mathematics 

# data[].attributes.subject
JournalAn Introduction to Financial Mathematics 

# data[].attributes.attachment_link.readable_text
On-Balance Volume

Technical indicators are used within technical analysis to gain insight into the supply and demand of securities. Indicators (such as volume) confirm price movement, and the probability that a price move will continue. The indicators can be used as a basis for trading, as they can form buy-and-sell signals. In this slideshow, we'll take you through seven common technical indicators that can help you round out your trading toolkit.

First up the on-balance volume indicator (OBV) is used to measure the positive and negative flow of volume in a security, relative to its price over time. It is a simple measure that keeps a cumulative total volume by adding or subtracting each period's volume, depending on the price movement. This measure expands on the basic volume measure by combining volume and price movement. The idea behind this indicator is that volume precedes price movement, so if a security is seeing an increasing OBV, it is a signal that volume is increasing on upward price moves. Decreases mean that the security is seeing increasing volume on down days.

Accumulation/Distribution Line

One of the most commonly used indicators to determine the money flow of a security is the accumulation/distribution line (A/D line). It is similar to on-balance volume indicator but, instead of only considering the closing price of the security for the period, it also takes into account the trading range for the period. This is thought to give a more accurate picture of money flow than the balance volume. The line trending up is a signal of increasing buying pressure, as the stock is closing above the halfway point of the range. The line trending downward is a signal of increasing selling pressure in the security. (For additional reading, see Trend-Spotting With the Accumulation/Distribution Line.)

Average Directional Index

The average directional index (ADX) is a trend indicator used to measure the strength and momentum of an existing trend. This indicator's main focus is not on the direction of the trend, but on the momentum. When the ADX is above 40, the trend is considered to have a lot of directional strength - either up or down, depending on the current direction of the trend. Extreme readings to the upside are considered to be quite rare compared to low readings. When the ADX indicator is below 20, the trend is considered to be weak or non-trending. (For more, see ADX: The Trend Strength Indicator.)

Aroon Indicator

The Aroon oscillator is a technical indicator used to measure whether a security is in a trend, and the magnitude of that trend. The indicator can also be used to identify when a new trend is set to begin. The indicator is comprised of two lines: an Aroon-up line and an Aroon-down line. A security is considered to be in an uptrend when the Aroon-up line is above 70 and above the Aroon-down line. The security is in a downtrend when the Aroon-down line is above 70 and above the Aroon-up line. (For more on this indicator, see Finding The Trend With Aroon.)

MACD

The moving average convergence divergence (MACD) is one of the most well-known and used indicators in technical analysis. It is used to signal both the trend and momentum behind a security. The indicator is comprised of two exponential moving averages (EMA), covering two different time periods, which help to measure momentum in the security. The idea behind this momentum indicator is to measure short-term momentum compared to long-term momentum to help determine the future direction of the asset. The MACD is simply the difference between these two moving averages, which (in practice) are generally a 12-period and 26-period EMA. (For more information, see Exploring Oscillators and Indicators: MACD.)

Relative Strength Index

The relative strength index (RSI) is used to signal overbought and oversold conditions in a security. The indicator is plotted between a range of zero-100, where 100 is the highest overbought condition and zero is the highest oversold condition. The RSI helps to measure the strength of a security's recent up moves, compared to the strength of its recent down moves. This helps to indicate whether a security has seen more buying or selling pressure over the trading period. (For more on this indicator, see Ride the RSI Rollercoaster.)

Stochastic Oscillator

The stochastic oscillator is another well-known momentum indicator used in technical analysis. In an upward trend, the price should be closing near the highs of the trading range. In a downward trend, the price should be closing near the lows of the trading range. When this occurs, it signals continued momentum and strength in the direction of the prevailing trend. The stochastic oscillator is plotted within a range of zero-100, and signals overbought conditions above 80 and oversold conditions below 20. (For more, see Trading Psychology And Technical Indicators.)

Tools Of The Trade: Conclusion

The goal of every short-term trader is to determine the direction of a given asset's momentum and to attempt to profit from it. There have been hundreds of technical indicators and oscillators developed for this specific purpose, and this slideshow has just revealed the tip of the iceberg. Now that you have been acquainted with a few of the basic indicators used in technical analysis, you can go forward and learn more - you are one step closer to being able to incorporate powerful technical indicators into your own strategies.

# data[].attributes.attachment_link.description
Technical indicators are used within technical analysis to gain insight into the supply and demand of securities. Indicators (such as volume) confirm price movement, and the probability that a price move will continue. The indicators can be used as a basis for trading, as they can form buy-and-sell signals.

# data[].attributes.body
You've seen movies in which frantic stock traders are buying a thousand shares of a hot stock or dumping shares of a plummeting stock. You've seen commercials for brokerage firms that claim to have exciting prospects and strong portfolios. And you've probably heard a hundred different ways to predict the rise and fall of the stock market.

How do these traders and firms predict which shares will hit big? How do they know when to sell?

The truth is there is no magical way to predict the stock market. Many issues affect rises and falls in share prices, whether gradual changes or sharp spikes. The best way to understand how the market fluctuates is to study trends.

In this article we will discuss stock market trends, which help investors identify what stocks to buy and when. Keeping track of upswings and downswings over the history of individual stocks, as well as being aware of market-wide trends, helps investors plan buying and selling.

Many factors affect prices in the stock market, including inflation, interest rates, energy prices, oil prices and international issues, such as war, crime, fraud and political unrest.

Sudden rises or drops in stock prices are often called spikes. Spikes are extremely difficult, if not impossible, to predict. Stock market trends are like the behavior of a person. After you study how a person reacts to different situations, you can make predictions about how that person will react to an event. Similarly, recognizing a trend in the stock market or in an individual stock will enable you to choose the best times to buy and sell.

Source:

# data[].attributes.attachment_link.readable_text
You've seen movies in which frantic stock traders are buying a thousand shares of a hot stock or dumping shares of a plummeting stock. You've seen commercials for brokerage firms that claim to have exciting prospects and strong portfolios. And you've probably heard a hundred different ways to predict the rise and fall of the stock market.

How do these traders and firms predict which shares will hit big? How do they know when to sell?

The truth is there is no magical way to predict the stock market. Many issues affect rises and falls in share prices, whether gradual changes or sharp spikes. The best way to understand how the market fluctuates is to study trends.

In this article we will discuss stock market trends, which help investors identify what stocks to buy and when. Keeping track of upswings and downswings over the history of individual stocks, as well as being aware of market-wide trends, helps investors plan buying and selling.

Many factors affect prices in the stock market, including inflation, interest rates, energy prices, oil prices and international issues, such as war, crime, fraud and political unrest.

Sudden rises or drops in stock prices are often called spikes. Spikes are extremely difficult, if not impossible, to predict. Stock market trends are like the behavior of a person. After you study how a person reacts to different situations, you can make predictions about how that person will react to an event. Similarly, recognizing a trend in the stock market or in an individual stock will enable you to choose the best times to buy and sell.

Go to the next page to learn about the whims of the stock market. You'll also find out what market analysts mean when they talk about bull markets and bear markets. Which animal is fiercer?

# data[].attributes.attachment_link.description
­You'v­e seen movies in which frantic stock traders are buying a thousand shares of a hot stock or dumping shares of a plummeting stock. You've seen commercials for brokerage firms that claim to have exciting prospects and strong portfolios. And you've probably heard a hundred different ways to predict the rise and fall of the stock market.

# data[].attributes.attachment_link.readable_text
You've seen movies in which frantic stock traders are buying a thousand shares of a hot stock or dumping shares of a plummeting stock. You've seen commercials for brokerage firms that claim to have exciting prospects and strong portfolios. And you've probably heard a hundred different ways to predict the rise and fall of the stock market.

How do these traders and firms predict which shares will hit big? How do they know when to sell?

The truth is there is no magical way to predict the stock market. Many issues affect rises and falls in share prices, whether gradual changes or sharp spikes. The best way to understand how the market fluctuates is to study trends.

In this article we will discuss stock market trends, which help investors identify what stocks to buy and when. Keeping track of upswings and downswings over the history of individual stocks, as well as being aware of market-wide trends, helps investors plan buying and selling.

Many factors affect prices in the stock market, including inflation, interest rates, energy prices, oil prices and international issues, such as war, crime, fraud and political unrest.

Sudden rises or drops in stock prices are often called spikes. Spikes are extremely difficult, if not impossible, to predict. Stock market trends are like the behavior of a person. After you study how a person reacts to different situations, you can make predictions about how that person will react to an event. Similarly, recognizing a trend in the stock market or in an individual stock will enable you to choose the best times to buy and sell.

Go to the next page to learn about the whims of the stock market. You'll also find out what market analysts mean when they talk about bull markets and bear markets. Which animal is fiercer?

# data[].attributes.attachment_link.description
­You'v­e seen movies in which frantic stock traders are buying a thousand shares of a hot stock or dumping shares of a plummeting stock. You've seen commercials for brokerage firms that claim to have exciting prospects and strong portfolios. And you've probably heard a hundred different ways to predict the rise and fall of the stock market.

# data[].attributes.headline
Isn't everyone trying to findgreat stocks?

# data[].attributes.subject
Isn't everyone trying to findgreat stocks?

# data[].attributes.body
Perhaps they are - but do they really know what they are looking for? Generally what many traders are doing is chasing the speculative return - the portion of share returns due to the expansion of the P/E multiple. Over a lifetime the speculative return is zero as PE ratios will always revert back to the mean. All that an investor can end up with in the end is the investment return of a stock which is entirely down to the growth in its profits and any dividends paid out . One can only win in the long run by tracking down and sticking with a great company with sustainably high returns on equity.

# data[].attributes.body
In order to find potentially great companies its worth using some stock screening option such as that at Stockopedia Premium to search for a consistent ROE of greater than a 12% average over the last 10 years with profit margins and asset turnover in the top quartile of their industry and only a moderate level of gearing.  Analysing the durability of the competitive advantage is the next step and only then is it worth keeping an eye on the share price. Inderstanding intrinsic and relative valuation will help finding the right buy point.

# data[].attributes.body
If profits are fully retained by a company - ₹10,000 invested at a 20% return (ROE) for 10 years becomes more than ₹60,000 and after another 10 years becomes ₹380,000. That's 38 times your money in 20 years.

This is the kind of business that Warren Buffett in his understated manner would say had 'good economics' and that's why it pays to play the stock market only in high ROE shares. You just can't get these kind of astonishing compounding returns in any low ROE business.

# data[].attributes.body
Profit is either paid out as dividends to shareholders or retained and reinvested in the business. Reinvesting this profit is where it gets interesting. That retained profit is added back to the starting equity to create an even larger capital base. If this capital can be reinvested at the same high return as the previous year then the next year's profits will be proportionally bigger. In a really great replicable and scalable business model this can repeat again and again over dozens of years… and the maths of what happens then can be startling.

# data[].attributes.headline
What is the key ratio required to find great stocks?

# data[].attributes.subject
What is the key ratio required to find great stocks?

# data[].attributes.body
If a company issues shares it starts with some equity in the bank (cash) that it invests to hopefully make a profit. The profit that the company generates as a percentage of the equity invested is known as the return on equity (ROE).

This simple profitability measure (that stock market websites so rarely seem to print) is the single most important ratio for finding huge wealth generating stocks. Why? The reason lies in what happens to the profit once its generated.

# data[].attributes.headline
What do you need to track down productive stocks?

# data[].attributes.subject
What do you need to track down productive stocks?

# data[].attributes.body
The finance industry has done such a good job of ensuring that share prices are divorced in investors minds from their underlying businesses that the most printed stock ratios on the web are always the Dividend Yield and the PE Ratio. These are great ratios, but useless for comparing companies on anything other than valuation grounds.

For investing in companies that can deliver extraordinary long term investment returns what one needs to understand is how profitable a company is, what the company does with that profit andhow a simple GCSE maths trick work wonders

# data[].attributes.attachment_link.readable_text
Warren Buffett, New York Times on November 25th 2012:

Suppose that an investor you admire and trust comes to you with an investment idea. "This is a good one," he says enthusiastically. "I'm in it, and I think you should be, too."

Would your reply possibly be this? "Well, it all depends on what my tax rate will be on the gain you're saying we're going to make. If the taxes are too high, I would rather leave the money in my savings account, earning a quarter of 1 percent." Only in Grover Norquist's imagination does such a response exist.

MBA final exam question: Explain the mistake in this paragraph.

How do we decide whether to invest in a project? Discounted cash flow.

For example, suppose you're thinking of building a factory (or starting a business). Once built, your best guess is that the factory will produce $10 profit every year. Discounting at a 5% required return, typical of stock market investments, the value of that profit stream is 1/.05=20 times the yearly profit, or $200. If the factory costs $150 to build, it's a good deal and will return more than its costs. You build it. If the factory costs $250 to build, you walk away.

Did you forget to put in after-tax cash flows? Whoops, that's a B- now at best. For example, if the tax rate is 50%, then your after-tax profits are only $5 each year. Now the value of the profit stream is only $100. The factory still costs $150 to build however, so now you'd be a fool to do it. It truly is better to leave your money in the bank earning a quarter of a percent.

Mr. Buffett made an elementary accounting mistake. How did he get it wrong? Implicitly, he is thinking that he pays $100, then gets back $100 for sure, and only the profit is taxed. He's thinking that a 5% rate of return gets cut to 2.5%, which is still better than 0.025%. But when you build a factory or start a business, you are not guaranteed return of principal. You only get the profits, if any. If the government taxes half the profits, that's like taking half the initial investment away.

This is perhaps an understandable mistake for a financial investor such as Mr. Buffett. In my example, the market value of the factory was $200, and falls to $100 when the tax is imposed. Mr. Buffett doesn't build factories or start businesses, he buys them. Now, Mr. Buffett -- ever the "value" investor -- can swoop in, buy the factory for $100, and a $5 per year after-tax cashflow generates the same 5% rate of return. But nobody will build new factories, and that's the economic damage.

Ok, now you get an A. Let's go for the A+.

Mr Buffett ignored risk. If somebody offers you a 5% rate of return, risk free, when Treasury bills offer you a quarter of 1 percent, his name is Madoff, not Buffett-Buddy.

Mr. Buffett wants you to think his investments are arbitrage opportunities, and a 2.5% arbitrage is as attractive as a 5% arbitrage. That's false. Investments involve bearing risk, and taxes make those investments directly worse.

Now, the effect of taxes here is subtle. Yes, a 50% tax rate cuts a 5% expected return down to 2.5%. But it also cuts volatility too. Isn't this just like deleveraging? Answer: no, because unless you're investing in green energy boodoggles only available to Administration cronies, the government takes your profits, but does not reimburse your losses.

If the investment makes 10%, you get 5%. If it makes 5%, you get 2.5%. But if it loses 10%, you lose 10%. It's a strictly worse investment when taxed. (Yes, you might be able to sell the losses if the IRS doesn't notice what you're up to... but now you know why Buffett is a " master of tax avoidance.")

And there is always another margin: If rates of return on investment look lousy, just stop investing at all and go on a consumption binge. The estate tax is a big subsidy to the round-the-world cruise and private jet industries.

I am really amazed by how this argument has evolved. Only a few months ago, supporters of the Administration's plans for higher tax rates admitted the plain fact that higher tax rates on investment are bad for growth. But, they argued that higher taxes would be good for other goals, like "fairness," redistribution, or winning elections important for other policies they like such as ACA. (These taxes are not going to put a dent in the deficit.) And we had a sensible argument about how bad the growth effects would be, and how long it would take for them to kick in.

Now they're trying to argue that taxes aren't bad for the economy at all. Some are suggesting higher investment tax rates are actually good for the economy. All in the face of the natural experiment playing out in front of us across the Atlantic. The contortions needed to make this argument are just embarrassing. As above.

It seems clear to me that the Administration wants to raise the tax rate on high income people for political reasons, whether or not they raise tax revenues from such people; witness the deafening silence about reforming the chaotic tax code. The Buffetts of the world who can exploit the loopholes in the tax code and lobby for more will do fine in the new world. But they shouldn't stoop to such obvious silliness to try to fool the rest of us that pain don't hurt.

(Thanks to Cliff Asness who brought this to my attention and suggested some of the arguments.)

# data[].attributes.attachment_link.description
Warren Buffett, New York Times on November 25th 2012: Suppose that an investor you admire and trust comes to you with an investment idea. "This is a good one," he says enthusiastically. "I'm in it, and I think you should be, too." Would your reply possibly be this?

# data[].attributes.body
Louis Bachelieron the Cenetary of Theorie De La Sp ´ Eculation

# data[].attributes.headline
Summary - Prediction of Stock Price Movement Using Continuous Time Models

# data[].attributes.subject
Summary - Prediction of Stock Price Movement Using Continuous Time Models

# data[].attributes.body
Mathematics plays a crucial role in functioning of financial markets and predicting the increment or decrement of the values of stocks.Complex financial systems can be described using mathematical concepts,known as mathematical models. Continuous time mathematical models have a particular value for potentially only an infinitesimally short amount of time.Some of its types are Black-Scholes model,input-output model,brownian model and monte carlo model. The Monte Carlo techniques are used for simulating stock price processes. For predicting the direction of stock price (as indicated by the hit ratios), the GBM (Geometric Brownian motion) model or VG (Variance Gamma) model can be used in any Monte Carlo method as most of the times we found no significant differences as evidenced from the t-tests. The hit ratios obtained are “near” random walk behavior. This hints that predicting stock price movement is a very challenging task. Since the results of the hit ratios are at the same level where even a random predictor can produce them, the results are justifiable. For predicting the stock price values using the monte carlo method, the GBM model performs well under the QMC (Quasi monte carlo) method and the VG model performs well under the LSMC (Least squares monte carlo) method. The finding has important implications in risk management simulations.

# data[].attributes.headline
Summary - Mathematics of Financial Markets

# data[].attributes.subject
Summary - Mathematics of Financial Markets

# data[].attributes.body
Mathematical Finance is the basis of a huge industry at the centre of modern global economic development, and the source of a great deal of mathematics. Further, the theory and applications have proceeded in parallel in a closely-linked way. Different types of mathematical models have helped in formulating different types of marketing strategies. Bachelier’s theory brought the idea of “Brownian Motion” in the year 1900. Bachelier’s main objective was to study the valuation of options. His ideas were supported by other scientists such as Einstein, Wiener, Kolmogorov and Kiyoshi. Paul-Andr´e Meyer’s supermartingale decomposition theorem opened the way to defining stochastic calculus. The net effect of these developments was to turn stochastic analysis accessible to science. In 1965 Paul Samuelson introduced the standard model, namely geometric Brownian motion and Ito calculus. The famous Black-Scholes formula was published in 1973. By 1980 arbitrage pricing theory was established and a close link with martingale theory was seen by Harrison, Kreps and Pliska. Various developments such as The Binomial Model, The Fundamental Theorem of Asset Pricing and many other models led to growth of the branch of Mathematical Finance.

# data[].attributes.headline
Journal - Prediction of Stock Price Movement Using
Continuous Time Models

# data[].attributes.subject
Journal - Prediction of Stock Price Movement Using
Continuous Time Models

# data[].attributes.headline
STOCK MARKET PERCENTAGES AND MATHEMATICS

# data[].attributes.subject
STOCK MARKET PERCENTAGES AND MATHEMATICS

# data[].attributes.body
Imagine a stock that falls fifty percent one day and rises fifty percent the next day. Seems like you’d have broken even, right? Wrong. This is the beauty of mathematics, and it occurs in the stock market all the time. While this shouldn’t be a significant problem for your investments, it can often be misleading and confusing when researching and analyzing stocks.

Let’s use the example of a recently volatile stock known as E-Trade Financial (ETFC). The stock price experienced a large sell off and dropped to $8.59 per share, a 58.7% drop. The next day a rally occurred in the stock market and E-Trade’s stock soared up 40.9%. This left the stock at $5.00 at the end of the day. This is a key example of how the percentage mathematics used in stock prices can easily be misleading to casual investors.

Now let’s break down this problem in simpler terms. Suppose you bought XYZ stock at $10 per share. It remains around $10 per share and suddenly it falls 80% one day due to a sell off and ends the day at a meager $2 per share. The next day, the aggregate stock market sentiment is the stock was oversold, so a rally occurs and the stock soars up 50%. If you were a long term investor during all this madness, you’d still be down significantly. A 50% rally in a $2 per share stock will only result in a $3 stock price. Which means despite the face value of 80%-50%=30%, you are actually down 70% on your investment of XYZ stock because the price per share ultimately went from $10 to $3.

# data[].attributes.headline
Using Linear Functions to Predict The Stock Market Math Unit

# data[].attributes.subject
Using Linear Functions to Predict The Stock Market Math Unit

# data[].attributes.attachment_link.title
Using Linear Functions to Predict The Stock Market Math Unit

# data[].attributes.body
Monte Carlo option model to calculate the value of an option with multiple sources of uncertainty or with complicated features. Monte Carlo Methods are particularly useful in the valuation of options with multiple sources of uncertainty or with complicated features, which would make them difficult to value through a straightforward Black-Scholes style or lattice based computation.

# data[].attributes.body
In finance, the binomial options pricing model (BOPM) provides a generalizable numerical method for the valuation of options. The binomial model was first proposed by Cox, Ross and Rubinstein in 1979. The model uses a “discrete-time” model of the varying price over time of the underlying financial instrument. In general, binomial options pricing models do not have closed-form.It is slower than the Black-Scholes model but more accurate.

# data[].attributes.body
The Black model is a variant of the Black-Scholes option pricing model. Its primary applications are for pricing options on future contracts, bond options, interest rate caps / floors, and swaptions. It was first presented in a paper written by Fisher Black in 1976.

# data[].attributes.body
The Brownian motion model for financial markets concerned with defining the concepts of financial assets and markets, portfolios, gains and wealth in terms of continuous-time stochastic process. Under this model, these assets have continuous prices evolving continuously in time and are driven by Brownian motion processes. This model requires an assumption of perfectly divisible assets and a frictionless market i.e. that no transaction costs occur either for buying or selling. Another assumption is that asset prices have no jumps, that is there are no surprises in the market.

# data[].attributes.body
In economics, an input–output model is a quantitative economic technique that represents the interdependencies between different branches of a national economy or different regional economies. Wassily Leontief  earned the Noble Price in Economics for his development of this model.

# data[].attributes.body
The Black–Schole model is a mathematical model of financial market having derivative  investment instruments. From the model, one can deduce the Black–Scholes formula, which gives a theoretical estimate of the price of European-styleoptions. The formula led to a boom in options trading markets around the world. lt is widely used, although often with adjustments and corrections, by options market participants. Many empirical tests have shown that the Black–Scholes price is very close to the observed prices.

# data[].attributes.body
A mathematical model is a description of a system using mathematical concepts. The process of developing a mathematical model is termed as mathematical modeling. Mathematical models are used in science, engineering, social science and finance. A model may help to explain a system and to study the effects of different components, and to make predictions about behaviour.

# data[].attributes.body
Algorithm Trading (automated trading, black-box trading, or simply algo-trading) is the process of using computers programmed to follow a defined set of instructions for placing a trade in order to generate better profits. The defined sets of rules are based on timing, price, quantity or any mathematical model.

# data[].attributes.attachment_link.readable_text
Algorithmic trading (automated trading, black-box trading or simply algo-trading) is the process of using computers programmed to follow a defined set of instructions (an algorithm) for placing a trade in order to generate profits at a speed and frequency that is impossible for a human trader. The defined sets of rules are based on timing, price, quantity or any mathematical model. Apart from profit opportunities for the trader, algo-trading makes markets more liquid and makes trading more systematic by ruling out the impact of human emotions on trading activities.

Suppose a trader follows these simple trade criteria:

Buy 50 shares of a stock when its 50-day moving average goes above the 200-day moving average. (A moving average is an average of past data points that smooths out day-to-day price fluctuations and thereby identifies trends.)

Sell shares of the stock when its 50-day moving average goes below the 200-day moving average.

Using this set of two simple instructions, it is easy to write a computer program that will automatically monitor the stock price (and the moving average indicators) and place the buy and sell orders when the defined conditions are met. The trader no longer needs to keep watch for live prices and graphs, or put in the orders manually. The algorithmic trading system automatically does it for him, by correctly identifying the trading opportunity.

Benefits of Algorithmic Trading

Algo-trading provides the following benefits:

trades executed at the best possible prices

instant and accurate trade order placement (thereby high chances of execution at desired levels)

trades timed correctly and instantly, to avoid significant price changes

reduced transaction costs (see the implementation shortfall example below)

simultaneous automated checks on multiple market conditions

reduced risk of manual errors in placing the trades

can be backtested, on available historical and real-time data,to see if it is a viable trading strategy

reduced possibility of mistakes by human traders based on emotional and psychological factors

The greatest portion of today's algo-trading is high frequency trading (HFT), which attempts to capitalize on placing a large number of orders at very fast speeds across multiple markets and multiple decision parameters, based on preprogrammed instructions.

Algo-trading is used in many forms of trading and investment activities, including:

Mid- to long-term investors or buy-side firms - pension funds, mutual funds, insurance companies - use it to purchase stocks in large quantities when they do not want to influence stock prices with discrete, large-volume investments.

Short-term traders and sell-side participants - market makers (such as brokerage houses),speculators and arbitrageurs - benefit from automated trade execution; in addition, algo-trading aids in creating sufficient liquidity for sellers in the market.

Systematic traders - trend followers, hedge funds or pairs traders (a market-neutral trading strategy that matches a long position with a short position in a pair of highly correlated instruments such as two stocks, exchange-traded funds (ETFs) or currencies) etc. - find it much more efficient to program their trading rules and let the program trade automatically.

Algorithmic trading provides a more systematic approach to active trading than methods based on a human trader's intuition or instinct.

Algorithmic Trading Strategies

Any strategy for algorithmic trading requires an identified opportunity that is profitable in terms of improved earnings or cost reduction. The following are common trading strategies used in algo-trading:

The most common algorithmic trading strategies follow trends in moving averages, channel breakouts, price level movements and related technical indicators. These are the easiest and simplest strategies to implement through algorithmic trading because these strategies do not involve making any predictions or price forecasts. Trades are initiated based on the occurrence of desirable trends, which are easy and straightforward to implement through algorithms without getting into the complexity of predictive analysis. The example mentioned above, of using the 50- and 200-day moving averages, is a popular trend-following strategy.

Buying a dual-listed stock at a lower price in one market and simultaneously selling it at a higher price in another market offers the price differential as risk-free profit or arbitrage. The same operation can be replicated for stocks vs. futures instruments, as price differentials do exist from time to time. Implementing an algorithm to identify such price differentials and placing the orders allows profitable opportunities in an efficient manner.

Index funds have defined periods of rebalancing to bring their holdings to par with their respective benchmark indices. This creates profitable opportunities for algorithmic traders, who capitalize on expected trades that offer 20 to 80 basis points profits depending on the number of stocks in the index fund, just before index fund rebalancing. Such trades are initiated via algorithmic trading systems for timely execution and best prices.

Mathematical Model Based Strategies

Proven mathematical models, like the delta-neutral trading strategy, allow trading on a combination of options and its underlying security. (Delta neutral is a portfolio strategy consisting of multiple positions with offsetting positive and negative deltas - a ratio comparing the change in the price of an asset, usually a marketable security, to the corresponding change in the price of its derivative - so that the overall delta of the assets in question totals zero.)

Mean reversion strategy is based on the idea that the high and low prices of an asset are a temporary phenomenon that revert to their mean value (average value) periodically. Identifying and defining a price range and implementing an algorithm based on that allows trades to be placed automatically when the price of asset breaks in and out of its defined range.

Volume Weighted Average Price (VWAP)

Volume weighted average price strategy breaks up a large order and releases dynamically determined smaller chunks of the order to the market using stock-specific historical volume profiles. The aim is to execute the order close to the Volume Weighted Average Price (VWAP).

Time weighted average price strategy breaks up a large order and releases dynamically determined smaller chunks of the order to the market using evenly divided time slots between a start and end time. The aim is to execute the order close to the average price between the start and end times, thereby minimizing market impact.

Until the trade order is fully filled, this algorithm continues sending partial orders, according to the defined participation ratio and according to the volume traded in the markets. The related "steps strategy" sends orders at a user-defined percentage of market volumes and increases or decreases this participation rate when the stock price reaches user-defined levels.

The implementation shortfall strategy aims at minimizing the execution cost of an order by trading off the real-time market, thereby saving on the cost of the order and benefiting from the opportunity cost of delayed execution. The strategy will increase the targeted participation rate when the stock price moves favorably and decrease it when the stock price moves adversely.

Beyond the Usual Trading Algorithms

There are a few special classes of algorithms that attempt to identify "happenings" on the other side. These "sniffing algorithms," used, for example, by a sell-side market maker, have the in-built intelligence to identify the existence of any algorithms on the buy side of a large order. Such detection through algorithms will help the market maker identify large order opportunities and enable them to benefit by filling the orders at a higher price. This is sometimes identified as high-tech front-running.

Technical Requirements for Algorithmic Trading

Implementing the algorithm using a computer program is the last part, accompanied by backtesting (trying out the algorithm on historical periods of past stock-market performance to see if using it would have been profitable). The challenge is to transform the identified strategy into an integrated computerized process that has access to a trading account for placing orders. The following are needed:

computer-programming knowledge to program the required trading strategy, hired programmers or pre-made trading software

network connectivity and access to trading platforms for placing the orders

access to market data feeds that will be monitored by the algorithm for opportunities to place orders

the ability and infrastructure to backtest the system once it's built - before it goes live on real markets

available historical data for backtesting, depending upon the complexity of rules implemented in the algorithm

Here is an example of how algorithmic trading works: Royal Dutch Shell (RDS) is listed on Amsterdam Stock Exchange (AEX) and London Stock Exchange (LSE). We start by building an algorithm to identify arbitrage opportunities. Here are few interesting observations:

AEX trades in euros, while LSE trades in British pound sterling

Due to the one-hour time difference, AEX opens an hour earlier than LSE, followed by both exchanges trading simultaneously for the next few hours and then trading only in LSE during the last hour as AEX closes

Can we explore the possibility of arbitrage trading on the Royal Dutch Shell stock listed on these two markets in two different currencies?

Requirements:

a computer program that can read current market prices

price feeds from both LSE and AEX

a forex (foreign exchange) rate feed for GBP-EUR

order-placing capability that can route the order to the correct exchange

backtesting capability on historical price feeds

The computer program should perform the following:

Read the incoming price feed of RDS stock from both exchanges.

Using the available foreign exchange rates, convert the price of one currency to the other.

If there exists a large enough price discrepancy (discounting the brokerage costs) leading to a profitable opportunity, then place the buy order on lower priced exchange and sell order on higher priced exchange.

If the orders are executed as desired, the arbitrage profit will follow.

Simple and easy! However, the practice of algorithmic trading is not that simple to maintain and execute. Remember, if you can place an algo-generated trade, so can the other market participants. Consequently, prices fluctuate in milli- and even microseconds. In the above example, what happens if your buy trade gets executed, but the sell trade doesn't because the sell prices change by the time your order hits the market? You will end up sitting with an open position, making your arbitrage strategy worthless.

There are additional risks and challenges: For example, system failure risks, network connectivity errors, time-lags between trade orders and execution, and, most important of all, imperfect algorithms. The more complex an algorithm, the more stringent backtesting is needed before it is put into action.

The Bottom Line

It's exciting to go for automation aided by computers with the goal of making money effortlessly. But one must make sure the system is thoroughly tested and required limits are set. Analytical traders should consider learning programming and building systems on their own, to be confident about implementing the right strategies in a foolproof manner. Cautious use and thorough testing of algo-trading can create profitable opportunities.

# data[].attributes.attachment_link.title
Basics of Algorithmic Trading: Concepts and Examples | Investopedia

# data[].attributes.attachment_link.description
Algorithmic trading (automated trading, black-box trading or simply algo-trading) is the process of using computers programmed to follow a defined set of instructions (an algorithm) for placing a trade in order to generate profits at a speed and frequency that is impossible for a human trader.

# data[].attributes.headline
Journal - Mathematics of Financial Markets

# data[].attributes.subject
Journal - Mathematics of Financial Markets

# data[].attributes.body
1. Mean

2. Median

3. Average

4. Standard Deviation

5. z-scores

6. p-value

# data[].attributes.attachment_link.description
Mr. Parikh discusses stock market basics, how manipulations take place, market bubbles etc.

# data[].attributes.body
Introduction to basics of stock market and mathematics

# data[].attributes.attachment_link.readable_text
Wall Street's wild swings last week helped skew both retirement portfolios and mathematical models of the financial markets. After all, a standard Gaussian function -a bell curve-would predict that such extreme dips and rises would be exceedingly rare and not prone to following one after the other on succeeding days.

Gaussian functions might be able to describe the distribution of grades in a big college class, with most students getting, say, B-/C+, and enable you to predict how many students will get A's or fail. But evidently, they do a poor job at explaining steep fluctuations in stock prices, although some economists and modelers think they are the best tool available to describe financial markets.

So can any math accurately describe market behavior and enable you to beat it? To find out, Scientific American spoke with statistical physicist H. Eugene Stanley of Boston University, a proponent of applying the approaches and concepts of physics to economics.

[ An edited transcript of the interview follows.]

Can mathematical models beat markets?
They haven't yet. Science is about empirical fact. There is no question that optimistic people think they can beat the market, but they don't do it consistently with mathematical models. No model can consistently predict the future. It can't possibly be.

So what can math predict?
What you can do is predict the risk of a given event. The risk just means the chance that something bad will happen, for example. That you can do with increasing accuracy because we have more and more data. It's like insurance companies: they cannot tell you when you are going to die, but they can predict the risk that you will die given the right information. You can do the same thing with stocks. If you lose less, you get ahead of those who lose more.

Why do economists and "quants"-those who use quantitative analysis to make financial trades-have such faith in their mathematical models then?
If they're just to reduce risk, then they're very valuable. If you're worried, for example, about the segment of the Chinese economy that deals with steel, you make a model of what that whole market is all about and then you see if we did this what would likely happen. They're right some of the time. It's better than nothing.

But when they have excessive faith in these models, it's not justified. Math starts with assumptions; the real world does not work that way. Economics, which calls itself a science, too often doesn't start with looking at empirical facts in any great detail. Fifteen years ago even the idea of looking at huge amounts of data did not exist. With a limited amount of data, the chance of a rare event is very low, which gave some economists a false sense of security that long-tail events did not exist.

Why do you argue that financial markets are ruled not by Gaussian functions but by power laws-relations in which the frequency of one event varies as a power of some attribute of that event and are generally more L-shape than bell shape?
For anything that is random and fluctuating, like a financial market, a Gaussian function is a wonderful way to make a histogram of the outcome. If the things that fluctuate are not correlated at all with one another, then it's demonstrable that a Gaussian function is the correct histogram.

The catch is: in a financial market, everything is correlated. The proof of that is that if the stock market were Gaussian, then you'd never have a flash crash. A Gaussian crash would be an event that goes out to maybe five standard deviations [that is, a rarity on par with one part in two million]. In markets, this is simply not true. There are events that are 100 standard deviations. Every economist knows for sure that these rare events occur and cannot be described by a Gaussian function. The question is: What are you going to do about it?

Power laws are simply way more accurate. If you don't know the risk, you are not going to make the right decision, and the economy is at risk from these big fluctuations. It's no surprise when they come. The only reason you have to wait awhile is because they are rare. Knowing that they will happen forces anyone prudent to have a plan for what to do if it happens.

The idea that it would be a power law that describes all the events, the tails and the middle is really a major contribution. It allows one to quantify risk. You can read off a plot of the law the numerical chance for a downturn of any given size. It's very small for something that is 100 standard deviations out but not so small for something that is 10 standard deviations out. In fact, the S&P 500 fluctuations-which if they were Gaussian, would pretty much be constrained to plus or minus five standard deviations-you find, in a 10-year period, the number of events that exceed five standard deviations is not just one, it's 64. And the number that exceeds 10 standard deviations is eight, and there was one event that exceeded 20 standard deviations. It looks like a power law, and that's what it is demonstrated to be when every trade of every stock is analyzed.

There are an awful lot of rare events and they're all ignored. This is not the best way I want my retirement funds invested.

Are algorithm-based trading programs causing these fluctuations, like in the "flash crash" in 2010, when the Dow Jones Industrial Index momentarily dropped roughly 1,000 points in minutes?
There is no question that a huge percentage of trades are done electronically by algorithms. Of course, the flash crash was triggered by that. But we had problems before [algorithm-based trading programs]. We've had lots of crashes.

The speed of a flash crash is vastly greater than the speed of crashes before. Things move fast because everybody knows everything all the time. In that sense, it's not the algorithm-based trading that moves the markets, it's that the information is so instantaneous.

Does this understanding of financial markets suggest anything about how to invest, like when to buy or sell?
It can't predict the future. The key thing is that it tells you not to listen to those who tell you now is the time to buy or sell if their advice is based on something wrong, as it sometimes is.

Is this all a result of the interlinked global financial system?
I believe so. The finances of every country are interlinked to the finances of every other country and, because they are interlinked, if one key players goes down then the other players know things aren't going to be as good. A useful analogy is coupled networks, which are far more susceptible to a cascade of failures than uncoupled networks.

Is there a remedy for preventing markets from affecting one another?
It would be nice if there were, but the system is going to be more fragile because it is so interlinked. Maybe something like a circuit breaker, something that slows trading down? There are two answers to that: one is that [a circuit breaker] is good and allows people to cool off, to realize the economy is still there. The opposite view is that we just pick up where we left off.

For something like the flash crash, you might try it out. If you lose five to 10 percent in the space of an hour, then you stop the market. Of course, stopping the market at a low point could do the opposite and convince everyone something bad is happening.

Can anything predict the market?
Let me tell you a story: two to the power of 10 is 1,024. One way to predict the market is to call up 1,024 trading places and tell half of them by week's end the market will be up and the other half that the market will be down. At the end of the week, forget about the half that knows you were wrong. Keep doing that for 10 weeks and, at the end, you will have called the market correctly for one person who will think you are a genius.

The economy is a very complex system-like the weather-that we understand bits of. You sure as heck can't decide on a Monday whether the weather will be nice on the coming weekend. No one can predict where the market will be at the end of the week.

# data[].attributes.attachment_link.description
Wall Street's wild swings last week helped skew both retirement portfolios and mathematical models of the financial markets. After all, a standard Gaussian function -a bell curve-would predict that such extreme dips and rises would be exceedingly rare and not prone to following one after the other on succeeding days.

# data[].attributes.attachment_link.readable_text
Pricing the Future: Finance, Physics, and the 300-Year Journey to the Black-Scholes Equation. By George Szpiro. Basic Books; 298 pages; $28 and £18.99. Buy from Amazon.com, Amazon.co.uk

OPTIONS and futures are almost as old as trade itself. From the farmer who sold his crop before the harvest to the merchant who bought at a set price in the future, the forerunners of today's markets can be traced to ancient Greece and Rome. Yet for centuries these markets remained stunted because of a simple question of valuation. What is the right to buy next year's olive crop worth? Answering this question took centuries of study of physics, botany and mathematics. When solved, it changed finance for ever.

The tale includes a fascinating succession of people who tried doggedly to master probability and markets. It is engagingly told by George Szpiro, a mathematician- turned-journalist, who flits between biographies and formulae. He begins with the futures and options markets of the tulip bubble of the 1630s. He looks at Napoleon's attempt to regulate trading with a modern-sounding ban on futures contracts and short sales. And he explores those whom history has forgotten, such as Jules Regnault, a self-taught broker's assistant who started working on the Paris Bourse in 1862. After seeing how share prices changed over time, he wrote a book on the subject and made a fortune trading shares. Regnault's writings have been largely forgotten, but his work foreshadowed modern financial theory.

Another great mind whose work was lost was Wolfgang Döblin. The son of a prominent German novelist of Jewish descent, Döblin fled Berlin to Paris in the 1930s. He obtained his PhD in mathematics at the Sorbonne, where he soon established himself as a pioneering mathematician and innovator in the field of probability. With war approaching, Döblin joined the French army in a gesture of gratitude to the country that had sheltered him. In his billet on the front-lines, he scribbled on a cheap school notebook, sketching out a formula that he sealed in an envelope and posted to the Académie des Sciences in Paris. Soon after, with his regiment surrounded and the French army in retreat, he burned his personal papers and, fearing what would happen if was captured by German soldiers, shot himself.

The envelope lay sealed in archives until May 2000, when it was found to contain the mathematical tools to describe the random movements of particles. Calculations such as these transformed people's understanding of physics and provided an important building block of the so-called Black-Scholes equation.

That equation, which Robert Merton, Myron Scholes and Fischer Black worked out in 1973, turned out to be a breakthrough that promised accurate assessments of the value of options, which are the right (but not the obligation) to buy or sell something at a particular price on some future date. Mr Merton and Mr Scholes were awarded the Nobel prize for their work on this in 1997. Black, who died in 1995, was also credited for his contribution.

The equation's publication led to a flowering of options markets and an explosion of trading on them. It also transformed investment banking and stockbroking. The affable trader who calculated prices and odds by the seat of his pants on the trading floor, much as a gambler did at the poker table, was supplanted by the "quant", a mathematician with a room full of computers and reams of data.

Yet the model has deep failings. Black-Scholes assumes that movements in share prices, like those of particles suspended in liquid, can be plotted using a Gaussian, or bell curve, distribution. Yet finance is filled with "fat tailed" events that occur far more frequently than predicted by this model of the physical world. Black-Scholes reached its zenith in 1998, just before the collapse of Long-Term Capital Management (LTCM), an investment firm backed by the two Nobel prize-winning economists.

LTCM failed when the yields on bonds issued by countries such as Russia and America began to diverge, something the models said was virtually impossible. A decade later the great financial crisis was ushered in by the simultaneous collapse of house prices across America, another event that the mathematical models said was virtually impossible. In both instances, financial firms quickly found themselves racking up daily losses that the computers said should occur only once in millions of years.

"Pricing the Future" is at its best when it skips through the parallel developments in physics, mathematics and economics that led to the equation, a development that Mr Szpiro compares to the discovery of the structure of DNA or Isaac Newton's laws of motion. Unfortunately, Mr Szpiro's narrative dodges some important questions that it ought to have delved into in detail. In just four pages the book describes, almost as an afterthought, the failings of the Black-Scholes model and the history of the past decade since the collapse of LTCM. Black-Scholes may well have been a great achievement, but histories of the financial crisis will treat it less than kindly. The quest to tame risk and price the future is far from over.

# data[].attributes.attachment_link.description
Pricing the Future: Finance, Physics, and the 300-Year Journey to the Black-Scholes Equation. By George Szpiro. Basic Books; 298 pages; $28 and £18.99. Buy from Amazon.com, Amazon.co.uk OPTIONS and futures are almost as old as trade itself.

# data[].attributes.attachment_link.title
I Know First Presentation (February 2013)

# data[].attributes.attachment_link.description
I Know First co-founder, Dr. Lipa Roitman delivers a lecture at Tel Aviv University about his company's advanced stock market forecasting algorithm.

# data[].attributes.body
A stock market or equity market is the aggregation of buyers and sellers (a loose network of economic transactions, not a physical facility or discrete entity) of stocks (also called shares); these may include securities listed on a stock exchange as well as those only traded privately.

Stocks can be categorized in various ways. One common way is by the country where the company is domiciled. For example, Nestle and Novartis are domiciled in Switzerland, so they may be considered as part of the Swiss stock market, although their stock may also be traded at exchanges in other countries.

At the close of 2012, the size of the world stock market (total market capitalisation) was about US$55 trillion.By country, the largest market was the United States (about 34%), followed by Japan (about 6%) and the United Kingdom (about 6%). This went up more in 2013.