Python for Finance, 3rd Edition

Chapter 13. Stochastics

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Stochastic models describe how quantities such as prices, interest rates, or risk factors evolve when randomness plays a central role. This chapter shows how to work with pseudo-random numbers, simulate stochastic processes, and use Monte Carlo methods for pricing and risk analysis in a way that integrates smoothly with the tools from the previous chapters.

You start with random number generation and basic distributions, then move to discrete-time and continuous-time processes, and finally use these building blocks to value options by simulation. Throughout the chapter you work in the IPython REPL and visualize key results with figures generated from scripts under code/figures/.

The chapter introduces the practical side of stochastics in finance: using numpy.random.Generator for reproducible samples, simulating random walks and geometric Brownian motion, implementing Monte Carlo valuation for European options, and reasoning about convergence as the number of simulated ...