Modern financial mathematics relies on the theory of random processes in time, reflecting the erratic fluctuations in financial markets.This book introduces the fascinating area of financial mathematics and its calculus in an accessible manner geared toward undergraduate students. Using little high-level mathematics, the author presents the basic methods for evaluating financial options and building financial simulations.
By emphasizing relevant applications and illustrating concepts with color graphics, Elementary Calculus of Financial Mathematics presents the crucial concepts needed to understand financial options among these fluctuations. Among the topics covered are the binomial lattice model for evaluating financial options, the Black Scholes and Fokker Planck equations, and the interpretation of Ito s formula in financial applications. Each chapter includes exercises for student practice and the appendices offer MATLAB?® and SCILAB code as well as alternate proofs of the Fokker Planck equation and Kolmogorov backward equation.
Audience: This book will be useful to teachers and undergraduate students of mathematics or finance.
Contents: Preface; List of Algorithms; Chapter 1: Financial Indices Appear to Be Stochastic Processes; Chapter 2: Ito s Stochastic Calculus Introduced; Chapter 3: The Fokker Planck Equation Describes the Probability Distribution; Chapter 4: Stochastic Integration Proves Ito s Formula; Appendix A: Extra MATLAB/SCILAB Code; Appendix B: Two Alternate Proofs; Bibliography; Index