What topics in statistics and mathematics do I need to understand thoroughly before I can start to dabble with stochastic volatility models and volatility arbitrage?
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Calculus, differential equations, linear algebra, and probability.
That will be enough to understand popular textbooks on the subject intended for upper-level undergraduates or first-year graduate students. To understand the research literature you will also need stochastic processes, stochastic calculus, real analysis, and potentially PDE.
Many other areas of applied math are relevant to more specific applications, for instance optimization and numerical methods.
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$\begingroup$ Thanks a lot. Can you narrow down what fields of probability? Also is a good knowledge of time series,ARIMA and GARCH necessary? Also if you can point out a beginner book for each of the above topics with examples relating to options? A general textbook on probability will probably have not finance specific examples. $\endgroup$ Commented Nov 21, 2014 at 15:20