An Elementary Introduction to Mathematical Finance
This textbook on the basics of option pricing is accessible to readers with limited mathematical training. It is for both professional traders and undergraduates studying the basics of finance. Assuming no prior knowledge of probability, Sheldon M. Ross offers clear, simple explanations of arbitrage, the Black-Scholes option pricing formula, and other topics such as utility functions, optimal portfolio selections, and the capital assets pricing model. Among the many new features of this third edition are new chapters on Brownian motion and geometric Brownian motion, stochastic order relations and stochastic dynamic programming, along with expanded sets of exercises and references for all the chapters.
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Normal Random Variables
Brownian Motion and Geometric Brownian Motion
Interest Rates and Present Value Analysis
Pricing Contracts via Arbitrage
The Arbitrage Theorem
The BlackScholes Formula
Additional Results on Options
Valuing by Expected Utility
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American put option approximation arbitrage theorem Assuming bank barrier option bets binomial Black–Scholes formula Brownian motion process concave function Consequently consider convex Date Gas Oil Date Price Log decreasing denote derivative determine drift parameter end-of-day price equal estimator European put option Example expected utility expected value expiration final fortune follows a geometric geometric Brownian motion given Hence independent initial price investor Lemma log(x maximal expected no-arbitrage cost nominal interest rate nonnegative normal random variable obtain optimal policy outcome payment payoff period portfolio preceding present value Price Log Difference problem Proof purchase put option rate of return result risk-neutral price risk-neutral probabilities Section security’s price sell share simulation Solution specified stochastic dominance stochastically strategy strike price Suppose tion trading days Unleaded Heating utility function variable with mean variance parameter Vn(x volatility parameter yields