The Mathematics of Finance: Modeling and Hedging / Edition 1by Victor Goodman, Joseph Stampfli, Joseph Stampfli
The Mathematics of Finance: Modeling and Hedging explains the process of computing derivative prices in terms of underlying equity prices, while at the same time provides readers with the mathematical tools and techniques to carry out that process. The authors help readers understand the process, develop insights into how derivatives are used, and comprehend… See more details below
The Mathematics of Finance: Modeling and Hedging explains the process of computing derivative prices in terms of underlying equity prices, while at the same time provides readers with the mathematical tools and techniques to carry out that process. The authors help readers understand the process, develop insights into how derivatives are used, and comprehend the risk associated with creating or trading these assets. These insights into derivative trading provide extra knowledge of how modern equity markets work.
Table of Contents
1. FINANCIAL MARKETS Markets and Math / Stocks and Their Derivatives / Pricing Futures Contracts / Bond Markets / Interest Rate Futures / Foreign Exchange 2. BINOMIAL TREES, REPLICATING PORTFOLIOS, AND ARBITRAGE Three Ways to Price a Derivative / The Game Theory Method / Replicating Portfolios / The Probabilistic Approach / Risk / Repeated Binomial Trees and Arbitrage / Appendix: Limits of the Arbitrage Method 3. TREE MODELS FOR STOCKS AND OPTIONS A Stock Model / Pricing a Call Option With the Tree Model / Pricing an American Option / Pricing an Exotic Option-Knockout Options / Pricing an Exotic Option-Lookback Options / Adjusting the Binomial Tree Model to Real-World Data / Hedging and Pricing the N-Period Binomial Model 4. USING SPREADSHEETS TO COMPUTE STOCK AND OPTION TREES Some Spreadsheet Basics / Computing European Option Trees / Computing American Option Trees / Computing a Barrier Option Tree / Computing N-Step Trees 5. CONTINUOUS TIME MODELS AND THE BLACK-SCHOLES FORMULA A Continuous-Time Stock Model / The Discrete Model / An Analysis of the Continuous Model / The Black-Scholes Formula / Derivation of the Black-Scholes Formula / Put-Call Parity / Trees and Continuous Models / The GBM Stock Price ModelA Cautionary Tale / Appendix: Construction of a Brownian Path 6. THE ANALYTIC APPROACH TO BLACK-SCHOLES Strategy for Obtaining the Differential Equation / Expanding V(S, t) / Expanding and Simplifying V(S[sub t1], t) / Finding a Portfolio / Solving the Black-Scholes Differential Equation / Options on Futures / Appendix: Portfolio Differentials 7. HEDGING Delta Hedging / Methods for Hedging a Stock or Portfolio / Implied Volatility / The Parameters Delta, Gamma, and Theta / Derivation of the Delta Hedging Rule / Delta Hedging a Stock Purchase 8. BOND MODELS AND INTEREST RATE OPTIONS Interest Rates and Forward Rates / Zero-Coupon Bonds / Swaps / Pricing and Hedging a Swap / Interest Rate Models / Bond Price Dynamics / A Bond Price Formula / Bond Prices, Spot Rates, and HJM / The Derivative Approach to HJM: The HGM Miracle / Appendix: Forward Rate Drift 9. COMPUTATIONAL METHODS FOR BONDS Tree Models for Bond Prices / A Binomial Vasicek Model: A Mean Reversion Model 10. CURRENCY MARKETS AND FOREIGN EXCHANGE RISKS The Mechanics of Trading / Currency Forwards: Interest Rate Parity / Foreign Currency Options / Guaranteed Exchange Rates and Quantos / To Hedge or Not to Hedgeand How Much 11. INTERNATIONAL POLITICAL RISK ANALYSIS Introduction / Types of International Risks / Credit Derivatives and the Management of Political Risk / Pricing International Political Risk / Two Models for Determining the Risk Premium / A Hypothetical Example of the JLT Model ANSWERS TO SELECTED EXERCISES / INDEX
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