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| List of Figures | |
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| List of Tables | |
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| List of Examples | |
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| Foreword | |
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| Preface to Volume III | |
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| Bonds and Swaps | |
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| Introduction | |
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| Interest Rates | |
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| Continuously Compounded Spot and Forward Rates | |
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| Discretely Compounded Spot Rates | |
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| Translation between Discrete Rates and Continuous Rates | |
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| Spot and Forward Rates with Discrete Compounding | |
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| LIBOR | |
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| Categorization of Bonds | |
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| Categorization by Issuer | |
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| Categorization by Coupon and Maturity | |
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| Characteristics of Bonds and Interest Rates | |
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| Present Value, Price and Yield | |
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| Relationship between Price and Yield | |
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| Yield Curves | |
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| Behaviour of Market Interest Rates | |
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| Characteristics of Spot and Forward Term Structures | |
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| Duration and Convexity | |
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| Macaulay Duration | |
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| Modified Duration | |
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| Convexity | |
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| Duration and Convexity of a Bond Portfolio | |
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| Duration-Convexity Approximations to Bond Price Change | |
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| Immunizing Bond Portfolios | |
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| Bonds with Semi-Annual and Floating Coupons | |
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| Semi-Annual and Quarterly Coupons | |
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| Floating Rate Notes | |
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| Other Floaters | |
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| Forward Rate Agreements and Interest Rate Swaps | |
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| Forward Rate Agreements | |
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| Interest Rate Swaps | |
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| Cash Flows on Vanilla Swaps | |
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| Cross-Currency Swaps | |
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| Other Swaps | |
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| Present Value of Basis Point | |
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| PV01 and Value Duration | |
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| Approximations to PV01 | |
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| Understanding Interest Rate Risk | |
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| Yield Curve Fitting | |
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| Calibration Instruments | |
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| Bootstrapping | |
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| Splines | |
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| Parametric Models | |
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| Case Study: Statistical Properties of Forward LIBOR Rates | |
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| Convertible Bonds | |
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| Characteristics of Convertible Bonds | |
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| Survey of Pricing Models for Convertible Bonds | |
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| Summary and Conclusions | |
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| Futures and Forwards | |
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| Introduction | |
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| Characteristics of Futures and Forwards | |
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| Interest Rate and Swap Futures | |
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| Bond Futures | |
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| Currency Futures and Forwards | |
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| Energy and Commodity Futures | |
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| Stock Futures and Index Futures | |
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| Exchange Traded Funds and ETF Futures | |
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| New Futures Markets | |
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| Theoretical Relationships between Spot, Forward and Futures | |
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| No Arbitrage Pricing | |
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| Accounting for Dividends | |
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| Dividend Risk and Interest Rate Risk | |
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| Currency Forwards and the Interest Rate Differential | |
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| No Arbitrage Prices for Forwards on Bonds | |
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| Commodity Forwards, Carry Costs and Convenience Yields | |
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| Fair Values of Futures and Spot | |
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| The Basis | |
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| No Arbitrage Range | |
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| Correlation between Spot and Futures Returns | |
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| Introducing Basis Risk | |
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| Basis Risk in Commodity Markets | |
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| Hedging with Forwards and Futures | |
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| Traditional 'Insurance' Approach | |
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| Mean-Variance Approach | |
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| Understanding the Minimum Variance Hedge Ratio | |
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| Position Risk | |
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| Proxy Hedging | |
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| Basket Hedging | |
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| Performance Measures for Hedged Portfolios | |
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| Hedging in Practice | |
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| Hedging Forex Risk | |
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| Hedging International Stock Portfolios | |
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| Case Study: Hedging an Energy Futures Portfolio | |
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| Hedging Bond Portfolios | |
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| Using Futures for Short Term Hedging | |
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| Regression Based Minimum Variance Hedge Ratios | |
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| Academic Literature on Minimum Variance Hedging | |
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| Short Term Hedging in Liquid Markets | |
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| Summary and Conclusions | |
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| Options | |
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| Introduction | |
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| Foundations | |
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| Arithmetic and Geometric Brownian Motion | |
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| Risk Neutral Valuation | |
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| Numeraire and Measure | |
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| Market Prices and Model Prices | |
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| Parameters and Calibration | |
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| Option Pricing: Review of the Binomial Model | |
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| Characteristics of Vanilla Options | |
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| Elementary Options | |
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| Put-Call Parity | |
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| Moneyness | |
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| American Options | |
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| Early Exercise Boundary | |
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| Pricing American Options | |
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| Hedging Options | |
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| Delta | |
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| Delta Hedging | |
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| Other Greeks | |
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| Position Greeks | |
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| Delta-Gamma Hedging | |
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| Delta-Gamma-Vega Hedging | |
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| Trading Options | |
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| Bull Strategies | |
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| Bear Strategies | |
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| Other Spread Strategies | |
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| Volatility Strategies | |
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| Replication of P&L Profiles | |
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| The Black-Scholes-Merton Model | |
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| Assumptions | |
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| Black-Scholes-Merton PDE | |
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| Is the Underlying the Spot or the Futures Contract? | |
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| Black-Scholes-Merton Pricing Formula | |
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| Interpretation of the Black-Scholes-Merton Formula | |
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| Implied Volatility | |
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| Adjusting BSM Prices for Stochastic Volatility | |
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| The Black-Scholes-Merton Greeks | |
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| Delta | |
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| Theta and Rho | |
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| Gamma | |
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| Vega, Vanna and Volga | |
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| Static Hedges for Standard European Options | |
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| Interest Rate Options | |
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| Caplets and Floorlets | |
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| Caps, Floors and their Implied Volatilities | |
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| European Swaptions | |
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| Short Rate Models | |
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| LIBOR Model | |
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| Case Study: Application of PCA to LIBOR Model Calibration | |
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| Pricing Exotic Options | |
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| Pay-offs to Exotic Options | |
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| Exchange Options and Best/Worst of Two Asset Options | |
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| Spread Options | |
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| Currency Protected Options | |
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| Power Options | |
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| Chooser Options and Contingent Options | |
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| Compound Options | |
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| Capped Options and Ladder Options | |
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| Look-Back and Look-Forward Options | |
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| Barrier Options | |
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| Asian Options | |
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| Summary and Conclusions | |
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| Volatility | |
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| Introduction | |
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| Implied Volatility | |
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| 'Backing Out' Implied Volatility from a Market Price | |
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| Equity Index Volatility Skew | |
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| Smiles and Skews in Other Markets | |
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| Term Structures of Implied Volatilities | |
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| Implied Volatility Surfaces | |
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| Cap and Caplet Volatilities | |
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| Swaption Volatilities | |
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| Local Volatility | |
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| Forward Volatility | |
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| Dupire's Equation | |
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| Parametric Models of Local Volatility | |
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| Lognormal Mixture Diffusion | |
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| Modelling the Dynamics of Implied Volatility | |
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| Sticky Models | |
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| Case Study I: Principal Component Analysis of Implied Volatilities | |
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| Case Study II: Modelling the ATM Volatility-Index Relationship | |
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| Case Study III: Modelling the Skew Sensitivities | |
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| Applications of Implied Volatility Dynamics to Hedging Options | |
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| Stochastic Volatility Models | |
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| Stochastic Volatility PDE | |
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| Properties of Stochastic Volatility | |
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| Model Implied Volatility Surface | |
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| Model Local Volatility Surface | |
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| Heston Model | |
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| GARCH Diffusions | |
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| CEV and SABR Models | |
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| Jumps in Prices and in Stochastic Volatility | |
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| Scale Invariance and Hedging | |
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| Scale Invariance and Change of Numeraire | |
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| Definition of Scale Invariance | |
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| Scale Invariance and Homogeneity | |
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| Model Free Price Hedge Ratios | |
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| Minimum Variance Hedging | |
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| Minimum Variance Hedge Ratios in Specific Models | |
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| Empirical Results | |
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| Trading Volatility | |
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| Variance Swaps and Volatility Swaps | |
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| Trading Forward Volatility | |
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| Variance Risk Premium | |
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| Construction of a Volatility Index | |
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| Effect of the Skew | |
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| Term Structures of Volatility Indices | |
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| Vix and Other Volatility Indices | |
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| Volatility Index Futures | |
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| Options on Volatility Indices | |
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| Using Realized Volatility Forecasts to Trade Volatility | |
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| Summary and Conclusion | |
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| Portfolio Mapping | |
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| Introduction | |
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| Risk Factors and Risk Factor Sensitivities | |
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| Interest Rate Sensitive Portfolios | |
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| Equity Portfolios | |
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| International Exposures | |
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| Commodity Portfolios | |
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| Options Portfolios | |
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| Orthogonalization of Risk Factors | |
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| Nominal versus Percentage Risk Factors and Sensitivities | |
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| Cash Flow Mapping | |
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| Present Value Invariant and Duration Invariant Maps | |
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| PV01 Invariant Cash Flow Maps | |
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| Volatility Invariant Maps | |
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| Complex Cash Flow Maps | |
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| Applications of Cash Flow Mapping to Market Risk Management | |
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| Risk Management of Interest Rate Sensitive Portfolios | |
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| Mapping Portfolios of Commodity Futures | |
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| Mapping an Options Portfolio to Price Risk Factors | |
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| Taylor Expansions | |
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| Value Delta and Value Gamma | |
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| Delta-Gamma Approximation: Single Underlying | |
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| Effect of Gamma on Portfolio Risk | |
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| Price Beta Mapping | |
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| Delta-Gamma Approximation: Several Underlyings | |
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| Including Time and Interest Rates Sensitivities | |
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| Mapping Implied Volatility | |
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| Vega Risk in Options Portfolios | |
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| Second Order Approximations: Vanna and Volga | |
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| Vega Bucketing | |
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| Volatility Beta Mapping | |
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| Case Study: Volatility Risk in FTSE 100 Options | |
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| Estimating the Volatility Betas | |
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| Model Risk of Volatility Mapping | |
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| Mapping to Term Structures of Volatility Indices | |
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| Using PCA with Volatility Betas | |
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| Summary and Conclusions | |
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| References | |
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| Index | |