Equity Hybrid Derivatives

Contents

Preface

PART ONE Modeling Volatility

CHAPTER 1 Theory

1.1 Concepts of Equity Modeling

      1.1.1 The Forward

      1.1.2 The Shape of Dividends to Come

      1.1.3 European Options on the Pure Stock Process

1.2 Implied Volatility

      1.2.1 Sticky Volatilities

1.3 Fitting the Market

      1.3.1 Arbitrage-Free Option Price Surfaces

      1.3.2 Implied Local Volatility

      1.3.3 European Payoffs

      1.3.4 Fitting the Market with Discrete Martingales

1.4 Theory of Replication

      1.4.1 Replication in Diffusion-Driven Markets

CHAPTER 2 Applications

2.1 Classic Equity Models

      2.1.1 Heston

      2.1.2 SABR

      2.1.3 Scott's Exponential Ornstein-Uhlenbeck Model

       2.1.4 Other Stochastic Volatility Models

      2.1.5 Extensions of Heston's Model

      2.1.6 Cliquets

      2.1.7 Forward-Skew Propagation

2.2 Variance Swaps, Entropy Swaps, Gamma Swaps

      2.2.1 Variance Swaps

      2.2.2 Entropy Swaps

      2.2.3 Gamma Swaps

2.3 Variance Swap Market Models

      2.3.1 Finite Dimensional Parametrizations

      2.3.2 Examples

      2.3.3 Fitting to the Market

PART TWO Equity Interest Rate Hybrids

CHAPTER 3 Short-Rate Models

3.1 Introduction

3.2 Ornstein-Uhlenbeck Models

3.3 Calibrating to the Yield Curve

       3.3.1 Hull-White Model

      3.3.2 Generic Ornstein-Uhlenbeck Models

3.4 Calibrating the Volatility

      3.4.1 Hull-White/Vasicek

      3.4.2 Generic Ornstein-Uhlenbeck Models

3.5 Pricing Hybrids

      3.5.1 Finite Differences

      3.5.2 Monte Carlo