This self-contained book is the first of a two-volume set providing a thorough introduction to quantitative finance, covering both theoretical and computational methods. This volume covers stochastic analysis, option pricing theory, optimal portfolio investment, and bond pricing. Computer simulations in Matlab and Python are provided to illustrate theoretical ideas. Background in mathematics is included in the appendices and the level of familiarity with computer programming is kept to a minimum.
Fundamental Concepts.- Financial Derivatives.- The Lebesgue Integral.-
Basic Probability Theory.- Conditional Expectation.- Stochastic Processes.-
Brownian Motion.- The Reflection Principle of Brownian Motion.- The Itô
Integral.- The Itô Formula.- Girsanovs Theorem.- Stochastic Differential
Equations.- The Feynman Kac Theorem.- The Binomial Tree Method for Option
Pricing.- The Black Scholes Merton Differential Equation.- The Martingale
Method.- Pricing of Vanilla Options.- Pricing of Exotic Options.- American
Options.- The Capital Asset Pricing Model.- Dynamic Programming.- Bond
Pricing.- Short Rate Models.- Numeraires.
Geon Ho Choe is Emeritus Professor at the 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.
