By Paul Wilmott
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Additional resources for Frequently asked questions in quantitative finance: including key models, important formul, popular contracts, essays and opinions, a history of quantitative finance, sundry lists, the commonest mistakes in quant finance, brainteasers, plenty of straight-
40 Frequently Asked Questions in Quantitative Finance CrashMetrics is another example of worst-case scenarios and uncertainty. A starting point for a mathematical deﬁnition of risk is simply as standard deviation. This is sensible because of the results of the Central Limit Theorem (CLT), that if you add up a large number of investments what matters as far as the statistical properties of the portfolio are just the expected return and the standard deviation of individual investments, and the resulting portfolio returns are normally distributed.
Mandelbrot, B & Hudson, R 2004 The (Mis)Behaviour of Markets: A Fractal View of Risk, Ruin and Reward. Proﬁle Books Chapter 2 FAQs 22 Frequently Asked Questions in Quantitative Finance What are the Different Types of Mathematics Found in Quantitative Finance? Short answer The ﬁelds of mathematics most used in quantitative ﬁnance are those of probability theory and differential equations. And, of course, numerical methods are usually needed for producing numbers. Example The classical model for option pricing can be written as a partial differential equation.
Discrete means that asset prices and/or time can only be incremented in ﬁnite chunks, whether a dollar or a cent, a year or a day. Continuous means that no such lower increment exists. The mathematics of continuous processes is often easier than that of discrete ones. But then when it comes to number crunching you have in any case to turn a continuous model into a discrete one. In discrete models we end up with difference equations. An example of this is the binomial model for option pricing. Time progresses in ﬁnite amounts, the time step.