Quantitative Methods for Finance with Simulations II: Numerical and Monte Carlo Integration

This self-contained book is the second of a two-volume set providing a thorough introduction to quantitative finance, covering both theoretical and computational methods. This volume covers numerical methods, including numerical solutions of ordinary and partial differential equations such as the Black–Scholes–Merton equation, as well as stochastic differential equations, Monte Carlo methods, estimation of implied volatility, stochastic volatility models, and Fourier transform methods for option pricing. The numerical methods are implemented in both Matlab and Python. Background in mathematics is included in the appendices and the level of familiarity with computer programming is kept to a minimum.