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 BlackScholesMerton 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.- Hestons 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.
Geon Ho Choe is Emeritus Professor at Korea Advanced Institute of Science and Technology (KAIST). He obtained his PhD in Mathematics at the University of California, Berkeley, in 1987. In a career spanning several decades, he supervised 21 PhD students. He is the author of the books Computational Ergodic Theory (Springer, 2005) and Stochastic Analysis for Finance with Simulations (Springer, 2016). He received the 2022 Korean Mathematical Society Education Award.
