This textbook provides an introduction to financial mathematics and financial engineering for undergraduate students who have completed a three- or four-semester sequence of calculus courses. It introduces the Theory of Interest, discrete and continuous random variables and probability, stochastic processes, linear programming, the Fundamental Theorem of Finance, option pricing, hedging, and portfolio optimization. The reader progresses from a solid grounding in multi-variable calculus through a derivation of the Black Scholes equation, its solution, properties, and applications.
Contents: The Theory of Interest; Discrete Probability; Normal Random Variables and Probability; The Arbitrage Theorem; Random Walks and Brownian Motion; Forwards and Futures; Options; Solution of the Black Scholes Equation; Derivatives of Black Scholes Option Prices; Hedging; Optimizing Portfolios; American Options.
