Stochastic Analysis for Finance with Simulations

The author's main interests are simulations of random phenomena in the areas of quantitative finance, random number generators, dynamical systems theory, and information theory. He has published a book titled "Computational Ergodic Theory".

“This book gives an introduction to financial mathematics. It presents also some background of mathematical facts necessary for understanding modern finance. … For the reader convenience, the book contains a detailed contents, a list of figures, a list of tables, a list of simulations, a list of acronyms and a list of used symbols.” (Jacek Jakubowski, zbMATH 1409.91002, 2019)“This excellent textbook is addressed to undergraduate and graduate students in mathematics and finance who want to study the main tools of stochastic calculus and its application to quantitative finance. Also, it can be used as a reference book for practitioners and professionals from the financial industry who want a better understanding of the theoretical aspects of stochastic calculus, and how it can be used in the pricing of financial derivatives.” (Carlos Vázquez Cendón, Mathematical Reviews, August, 2017)

• Preface.- Acknowledgements.- List of Figures.- List of Tables.- List of Simulations.- 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. Appendices.- Solutions for Selected Problems.- Glossary.- References.- Index.