Chapter 10. Stochastics

Predictability is not how things will go, but how they can go.

Raheel Farooq

Nowadays, stochastics is one of the most important mathematical and numerical disciplines in finance. In the beginning of the modern era of finance, mainly in the 1970s and 1980s, the major goal of financial research was to come up with closed-form solutions for, e.g., option prices given a specific financial model. The requirements have drastically changed in recent years in that not only is the correct valuation of single financial instruments important to participants in the financial markets, but also the consistent valuation of whole derivatives books, for example. Similary, to come up with consistent risk measures across a whole financial institution, like value-at-risk and credit value adjustments, one needs to take into account the whole book of the institution and all its counterparties. Such daunting tasks can only be tackled by flexible and efficient numerical methods. Therefore, stochastics in general and Monte Carlo simulation in particular have risen to prominence.

This chapter introduces the following topics from a Python perspective:

Random number generation
It all starts with (pseudo)random numbers, which build the basis for all simulation efforts; although quasirandom numbers, e.g., based on Sobol sequences, have gained some popularity in finance, pseudorandom numbers still seem to be the benchmark.
In finance, two simulation tasks are of particular ...

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