Stochastic Finance with Python

Journey through the world of stochastic finance from learning theory, underlying models, and derivations of financial models (stocks, options, portfolios) to the almost production-ready Python components under cover of stochastic finance. This book will show you the techniques to estimate potential financial outcomes using stochastic processes implemented with Python. The book starts by reviewing financial concepts, such as analyzing different asset types like stocks, options, and portfolios. It then delves into the crux of stochastic finance, providing a glimpse into the probabilistic nature of financial markets. You’ll look closely at probability theory, random variables, Monte Carlo simulation, and stochastic processes to cover the prerequisites from the applied perspective. Then explore random walks and Brownian motion, essential in understanding financial market dynamics. You’ll get a glimpse of two vital modelling tools used throughout the book - stochastic calculus and stochastic differential equations (SDE). Advanced topics like modeling jump processes and estimating their parameters by Fourier-transform-based density recovery methods can be intriguing to those interested in full-numerical solutions of probability models. Moving forward, the book covers options, including the famous Black-Scholes model, dissecting it from both risk-neutral probability and PDE perspectives. A chapter at the end also covers the discovery of portfolio theory, beginning with mean-variance analysis and advancing to portfolio simulation and the efficient frontier.