Quantitative Methods for Finance with Simulations II

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.

Numerical Methods for Ordinary Differential Equations. - The Second Order Linear Partial Differential Equations. - Numerical Methods for Elliptic Equations. - Numerical Methods for Parabolic Equations. - Numerical Methods for Hyperbolic Equations. - Numerical Methods for the Black Scholes Merton Equation. - Numerical Methods for Pricing American Put Options. - Numerical Methods for Stochastic Differential Equations. - Multidimensional Brownian Motion. - Multidimensional Itô Calculus. - The Multi-asset Black Scholes Merton Equation. - Random Numbers. - The Monte Carlo Method. - The Monte Carlo Method for Option Pricing. - Historical Volatility. - Numerical Methods for Finding Zeros of a Function. - Numerical Computation of Implied Volatility. - Recursive Methods for Pricing of Asian Options. - A Control Variate Method Based On Conditioning. - Stochastic Volatility. - Heston s Stochastic Volatility Model. - Option Pricing Formula Under the Heston Model. - Numerical Methods for the Heston Formula. - Fourier Transforms for Stochastic Processes. - Option Pricing by the Fourier Transform.