Modelling and Hedging Equity Derivatives

Introduction

Mathematical Fundamentals

A Review of Probability Theory and Stochastic Calculus

The Black-Scholes Equity Model

Extensions to Black-Scholes

The Clark Formula

The Hybrid Model

The Multi-Currency Hybrid Model

Closed-Form Solutions for Standard Products

Basic Products

American Options

Digital Options

Barrier Options

Asian Options

Closed-Form Solutions for Non-Standard Products

Lookback Options

Fade-In Options

Fade-In Barrier Options

Chooser Options

Prolongation Options

Improving Options

Power and Powered Options

Compound Options

Closed-Form Solutions for Multi-Asset Products

Exchange Options

Relative Digital Options

Relative Outperformance Options

Outperformance options

European Digital Option on Best or Worst of Two Assets

Best or Worst of Several Assets

Basket Options

Hindsight Options

Outside Barrier Options

Outside Digital Options

Closed-Form Fixed Income and Hybrid Products

Bond Options and Swaptions

Caps and Floors

European Options (Merton Formula)

Equity/Bond Outperformance Options

The Tree Approach

Setting up the Tree

Option Pricing Using Trees

Barrier Options

Bermudan Asian Options

Convertible Bonds

Monte Carlo Methods

The Basic Method

Speeding Up Monte Carlo

Generic Monte Carlo Pricing

Hybrid Monte Carlo

Monte Carlo for American Options

A Partial Differential Equation Solver

Discretisation of the PDE

Boundary Conditions

Moving Barriers

Range and Fade-In Options

American Options

Discrete Dividends

Model Calibration

Further Modelling Issues

Calibration of the Extended Vasicek Model

Basket and Asian Underlyings

Volatility Smile

Hedging

Hedging and Risk Management

Pricing and Hedging European Options Under Transaction Costs

Hedging of Specific Products

Implementation Issues

The Context of a Model Library

Library Interface Design

Internal design

Appendix: Useful Formulas

Bibliography