Modelling and Hedging Equity Derivatives

Financial Risk Management

Modelling and Hedging Equity Derivatives

Edited by Oliver Brockhaus · Andrew Ferraris · Christoph Gallus · Douglas Long · Reiner Martin · Marcus Overhaus
Risk Books June 1999

Specifications

ISBN-13
9781899332342
Publisher
Risk Books
Publication
June 1999
Format
Paperback
Jurisdiction
International ? Countri(es) for reference only

Details

A definitive reference on the maths, techniques and practical approaches to modelling&hedging equity derivatives.

  • In-depth analysis of probability theory and stochastic calculus as well as alternative approaches for products that cannot be valued within these frameworks
  • Provides a practical approach for hedging equity products beyond delta hedging and discusses in detail practical software implementation issues


Table of Contents

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

Reviews

“The mathematical discussions are sophisticated, practical and insightful. Anyone who is or wants to be a financial engineer in the equity markets must read this book.“

Glyn Holton, Contingency Analysis

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