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Preface | |

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Introduction | |

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Forward Contracts | |

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Futures Contracts | |

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Options | |

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Other Derivatives | |

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Types of Traders | |

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Those Big Losses | |

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Futures Markets and the Use of Futures for Hedging | |

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Trading Futures Contracts | |

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Specification of the Futures Contract | |

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Operation of Margins | |

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Newspaper Quotes | |

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Convergence of Futures Price to Spot Price | |

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Settlement | |

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Regulation | |

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Hedging Using Futures | |

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Optimal Hedge Ratio | |

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Rolling the Hedge Forward | |

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Accounting and Tax | |

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Forward and Futures Prices | |

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Some Preliminaries | |

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The Forward Price for an Investment Asset | |

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The Effect of Known Income | |

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The Effect of a Known Dividend Yield | |

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Value of a Forward Contract | |

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Forward Prices versus Futures Prices | |

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Stock Index Futures | |

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Foreign Currencies | |

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Futures on Commodities | |

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The Cost of Carry | |

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Delivery Options | |

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Futures Prices and the Expected Future Spot Price | |

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Assets Providing Dividend Yields | |

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Proof That Forward and Futures Prices Are Equal When Interest Rates Are Constant | |

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Interest Rates and Duration | |

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Types of Rates | |

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Zero Rates | |

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Bond Pricing | |

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Determining Zero Rates | |

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Forward Rates | |

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Forward-Rate Agreements | |

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Theories of the Term Structure | |

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Day Count Conventions | |

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Quotations | |

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Interest Rate Futures | |

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Treasury Bond Futures | |

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Eurodollar Futures | |

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Duration | |

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Duration-Based Hedging Strategies | |

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Limitations of Duration | |

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Swaps | |

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Mechanics of Interest Rate Swaps | |

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The Comparative Advantage Argument | |

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Valuation of Interest Rate Swaps | |

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Currency Swaps | |

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Valuation of Currency Swaps | |

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Other Swaps | |

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Credit Risk | |

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Construction of Zero-Coupon LIBOR Curve | |

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Options Markets | |

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Underlying Assets | |

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Specification of Stock Options | |

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Newspaper Quotes | |

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Trading | |

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Commissions | |

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Margins | |

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The Options Clearing Corporation | |

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Regulation | |

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Taxation | |

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Warrants, Executive Stock Options, and Convertibles | |

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Properties of Stock Option Prices | |

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Factors Affecting Option Prices | |

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Assumptions and Notation | |

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Upper and Lower Bounds for Option Prices | |

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Put--Call Parity | |

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Early Exercise: Calls on a Non-Dividend-Paying Stock | |

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Early Exercise: Puts on a Non-Dividend-Paying Stock | |

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Relationship Between American Put and Call Prices | |

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The Effect of Dividends | |

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Empirical Research | |

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Trading Strategies Involving Options | |

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Strategies Involving a Single Option and a Stock | |

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Spreads | |

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Combinations | |

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Other Payoffs | |

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Introduction to Binomial Trees | |

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A One-Step Binomial Model | |

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Risk-Neutral Valuation | |

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Two-Step Binomial Trees | |

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A Put Option Example | |

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American Options | |

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Delta | |

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Matching Volatility with u and d | |

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Binomial Trees in Practice | |

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Model of the Behavior of Stock Prices | |

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The Markov Property | |

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Continuous Time Stochastic Processes | |

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The Process for Stock Prices | |

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Review of the Model | |

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The Parameters | |

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Ito's Lemma | |

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Derivation of Ito's Lemma | |

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The Black--Scholes Model | |

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Lognormal Property of Stock Prices | |

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The Distribution of the Rate of Return | |

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Volatility | |

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Concepts Underlying the Black--Scholes--Merton Differential Equation | |

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Derivation of the Black--Scholes--Merton Differential Equation | |

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Risk-Neutral Valuation | |

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Black--Scholes Pricing Formulas | |

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Cumulative Normal Distribution Function | |

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Warrants Issued by a Company on Its Own Stock | |

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Implied Volatilities | |

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The Causes of Volatility | |

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Dividends | |

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Proof of Black--Scholes--Merton Formula | |

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Exact Procedure for Calculating Values of American Calls on Dividend-Paying Stocks | |

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Calculation of Cumulative Probability in Bivariate Normal Distribution | |

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Options on Stock Indices, Currencies, and Futures | |

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Results for a Stock Paying a Continuous Dividend Yield | |

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Option Pricing Formulas | |

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Options on Stock Indices | |

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Currency Options | |

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Futures Options | |

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Valuation of Futures Options Using Binomial Trees | |

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A Futures Price as a Stock Paying a Continuous Dividend Yield | |

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Black's Model for Valuing Futures Options | |

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Comparison of Futures Option and Spot Option Prices | |

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Derivation of Differential Equation Satisfied by a Derivative Dependent on a Stock Providing a Continuous Dividend Yield | |

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Derivation of Differential Equation Satisfied by a Derivative Dependent on a Futures Price | |

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The Greek Letters | |

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Example | |

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Naked and Covered Positions | |

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A Stop-Loss Strategy | |

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Delta Hedging | |

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Theta | |

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Gamma | |

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Relationship among Delta, Theta, and Gamma | |

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Vega | |

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Rho | |

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Hedging in Practice | |

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Scenario Analysis | |

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Portfolio Insurance | |

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Stock Market Volatility | |

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Taylor Series Expansions and Hedge Parameters | |

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Value at Risk | |

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Daily Volatilities | |

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Calculation of VaR in Simple Situations | |

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A Linear Model | |

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How Interest Rates Are Handled | |

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When the Linear Model Can Be Used | |

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A Quadratic Model | |

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Monte Carlo Simulation | |

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Historical Simulation | |

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Stress Testing and Back-Testing | |

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Principal Components Analysis | |

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Use of the Cornish-Fisher Expansion to Estimate VaR | |

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Estimating Volatilities and Correlations | |

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Estimating Volatility | |

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The Exponentially Weighted Moving Average Model | |

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The GARCH (1,1) Model | |

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Choosing Between the Models | |

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Maximum Likelihood Methods | |

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Using GARCH (1,1) to Forecast Future Volatility | |

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Correlations | |

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Numerical Procedures | |

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Binomial Trees | |

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Using the Binomial Tree for Options on Indices, Currencies, and Futures Contracts | |

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Binomial Model for a Dividend-Paying Stock | |

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Extensions of the Basic Tree Approach | |

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Alternative Procedures for Constructing Trees | |

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Monte Carlo Simulation | |

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Variance Reduction Procedures | |

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Finite Difference Methods | |

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Analytic Approximation to American Option Prices | |

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Analytic Approximation to American Option Prices | |

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Volatility Smiles and Alternatives to Black-Scholes | |

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Preliminaries | |

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Foreign Currency Options | |

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Equity Options | |

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The Volatility Term Structure | |

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Volatility Matrices | |

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Relaxing the Assumptions in Black-Scholes | |

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Alternative Models for Stock Options | |

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Pricing Models Involving Jumps | |

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Stochastic Volatility Models | |

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Empirical Research | |

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Pricing Formulas for Alternative Models | |

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Exotic Options | |

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Types of Exotic Options | |

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Path-Dependent Derivatives | |

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Lookback Options | |

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Barrier Options | |

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Options on Two Correlated Assets | |

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Implied Trees | |

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Hedging Issues | |

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Static Options Replication | |

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Calculation of the First Two Moments of Arithmetic Averages and Baskets | |

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Extensions of the Theoretical Framework for Pricing Derivatives: Martingales and Measures | |

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The Market Price of Risk | |

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Derivitives Dependent on Several State Variables | |

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Derivatives Dependent on Commodity Prices | |

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Martingales and Measures | |

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Alternative Choices for the Numeraire | |

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Extension to Multiple Independent Factors | |

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Applications | |

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Change of Numeraire | |

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Quantos | |

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Siegel's Paradox | |

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Generalization of Ito's Lemma | |

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Derivation of the General Differential Equation Satisfied by Derivatives | |

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Interest Rate Derivatives: The Standard Market Models | |

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Black's Model | |

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Bond Options | |

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Interest Rate Caps | |

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European Swap Options | |

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Generalizations | |

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Convexity Adjustments | |

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Timing Adjustments | |

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When Is an Adjustment Necessary? | |

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Accrual Swaps | |

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Spread Options | |

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Hedging Interest Rate Derivatives | |

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Proof of the Convexity Adjustment Formula | |

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Interest Rate Derivatives: Models of the Short Rate | |

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Equilibrium Models | |

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One-Factor Equilibrium Model | |

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The Rendleman and Bartter Model | |

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The Vasicek Model | |

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The Cox, Ingersoll, and Ross Model | |

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Two-Factor Equilibrium Models | |

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No-Arbitrage Models | |

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The Ho and Lee Model | |

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The Hull and White Model | |

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Options on Coupon-Bearing Bonds | |

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Interest Rate Trees | |

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A General Tree-Building Procedure | |

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Nonstationary Models | |

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Calibration | |

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Hedging Using a One-Factor Model | |

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Forward Rates and Futures Rates | |

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Interest Rate Derivatives: More Advanced Models | |

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Two-Factor Models of the Short Rate | |

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The Heath, Jarrow, and Morton Approach | |

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The LIBOR Market Model | |

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Mortgage-Backed Securities | |

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The A(t, T), [sigma][rho] and [thetas](t) Functions in the Two-Factor Hull-White Model | |

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Credit Risk | |

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The Probability of Default and Expected Losses | |

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Adjusting the Prices of Derivatives to Reflect Counterparty Default Risk | |

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Credit Value at Risk | |

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Credit Derivatives | |

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Valuation of Convertible Bonds | |

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Manipulation of the Matrices of Credit Rating Changes | |

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Glossary of Notation | |

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Glossary of Terms | |

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DerivaGem Software | |

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Major Exchanges Trading Futures and Options | |

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Table for N(x) when x [less than or equal] 0 | |

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Table for N(x) when x [greater than or equal] 0 | |

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Author Index | |

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Subject Index | |