Stochastic Analysis for Finance with Simulations 2016 1st ed. 2016

This book is an introduction to stochastic analysis and quantitative finance; it includes both theoretical and computational methods. Topics covered are stochastic calculus, option pricing, optimal portfolio investment, and interest rate models. Also included are simulations of stochastic phenomena, numerical solutions of the Black-Scholes-Merton equation, Monte Carlo methods, and time series. Basic measure theory is used as a tool to describe probabilistic phenomena. The level of familiarity with computer programming is kept to a minimum. To make the book accessible to a wider audience, some background mathematical facts are included in the first part of the book and also in the appendices. This work attempts to bridge the gap between mathematics and finance by using diagrams, graphs and simulations in addition to rigorous theoretical exposition. Simulations are not only used as the computational method in quantitative finance, but they can also facilitate an intuitive and deeper understanding of theoretical concepts. Stochastic Analysis for Finance with Simulations is designed for readers who want to have a deeper understanding of the delicate theory of quantitative finance by doing computer simulations in addition to theoretical study. It will particularly appeal to advanced undergraduate and graduate students in mathematics and business, but not excluding practitioners in finance industry.Fundamental Concepts.- Financial Derivatives.- The Lebesgue Integral.- Basic Probability Theory.- Conditional Expectation.- Stochastic Processes.- Brownian Motion.- Girsanov"s Theorem.- The Reflection Principle of Brownian Motion.- The Ito Integral.- The Ito Formula.- Stochastic Differential Equations.- The Feynmann-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.- Interest Rate Models.- Numeraires.- Numerical Estimation of Volatility.- Time Series.- Random Numbers.- The Monte Carlo Method for Option Pricing.- Numerical Solution of the Black-Scholes-Merton Equation.- Numerical Solution of Stochastic Differential Equations