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Foreign Exchange Risk

Edited By Jurgen Hakala and Uwe Wystup

Overview

Provides all the vital quantitative tools for foreign exchange options in a clear and logical manner.

Publish date: 1 Feb 2002

Availability: In stock

£145.00
OR

Book description

  • Covers the financial management of foreign exchange risk together with analysis of different methods for mitigating and controlling cross currency price differentials
  • Shows how both market risk and model risk can be managed by choosing a suitable pricing model
  • Presents products, pricing models, tools and strategies as well as numerical techniques for practical implementation
  • Contains leading research, published for the first time, concerned primarily with FX derivatives

Book details

ISBN
9781899332373
Publish date
1 Feb 2002
Format
Size
A4

Editor biography

Jurgen Hakala and Uwe Wystup

Table of contents

Part I. Market: Products and Basics

Vanilla Options

Model and payoff

Value

Greeks

Identities

Quotation

Dual Black-Scholes partial differential equation

Retrieving the arguments

Greeks in terms of deltas

Volatility Management

Market risk of foreign exchange options

Historic volatility vs implied volatility

Market data

Volatility smile

Risk reversals and butterflies

Shape of the smile

Reasons for the smile

Term structure models and formulae

Wing shifts

Term structure of volatility at-the-money

Handling Differing Expiry and Delivery Dates

The Impact of Non-business Days on the Pricing of Options

Introduction

Model and results

Barrier Options – An Overview

What is a barrier option?

The popularity of barrier options

Barrier option crisis in 1994-96, questions about exotics in general

Types of barriers

How the barrier is monitored (continuous vs discrete) and how this influences the price

How breaching the barrier is determined

Hedging methods, coping with high delta and gamma

How large barrier contracts affect the market

Difference between market prices and theoretical Black-Scholes values explained

The Pricing of First Generation Exotics

Introduction

Single barrier options

Digital options

One-touch options

Double no-touch options

Corridors

Double barrier options

Fade-in-out options

Slide-in corridor

The Pricing of Second Generation Exotics

Introduction

Forward-start options

Ratchet options

Power options

Installment options

Stairs options

Compound on forward start strategy

Options on the minimum/maximum

Generalized options on the minimum/maximum

Quanto Options

Introduction

Quanto forward

Quanto European plain vanilla

Quanto forward start plain vanilla

Quanto power option

No-Arbitrage Bounds and Static Hedging of Compound Options

Compound options

Put-call parity and no-arbitrage bounds for compound options

Value of compound options in the Black-Scholes model

Hedging of compound options

Static hedging of compound options

Taking a Corporate View: Zero Cost Structures

Products and markets

Pricing

Conclusion

Probability Density Functions and Related Tools

Motivation

The probability density function

First exit times

A Note on Forward and Backward Partial Differential Equations for Derivative

Contracts with Forwards as Underlyings

Introduction

Forward and backward equations

Forward-based derivation of backward and forward partial differential equations

Summary

Part II. Risk Management

Efficient Computation of Option Price Sensitivities Using Homogeneity and Other Tricks

Introduction

Fundamental properties

European options in the Black-Scholes model

The one-dimensional case

A European claim in the two-dimensional Black-Scholes model

Summary

How the Greeks Would Have Hedged Correlation Risk of Foreign Exchange Options

Introduction

Foreign exchange market model

The extension beyond triangular markets

Geometric interpretation

Hedging correlation risk

Part III. Models and Applications to Exotic Options

An Arithmetic Average Model with Applications to Pricing Asian and Basket Options

Introduction

Moment matching for the arithmetic spot

Alternative method of pricing using stochastic Taylor expansion

Asian options

Basket options

Conclusion

Finite Differences

Introduction

Black-Scholes framework

Stochastic volatility models

Path dependence at discrete points in time

The Greeks

Monte Carlo Simulations and Variance Reduction Techniques

Introduction

The method

Path-independent derivatives

Variance reduction methods

Barrier options

Stochastic volatility

Calculating the Greeks

Quasi-Random Numbers and their Application to Pricing Basket and Lookback Options

Introduction

Some quasi-random sequences and a qualitative description

The discrepancy, a quantitative description

Independent quasi-random numbers

Examples of Monte Carlo integration with quasi-random numbers

Convergence

Basket options

Lookback options

Conclusion

Quasi-Monte Carlo Techniques for the Valuation of Contingent Claims on Several Assets

Introduction

Problem and notation

The methods

Numerical results

Summary

Binomial Trees in One and Two Dimensions

One step model

The martingale measure

Implementation

Convergence

Barrier options

Binomial trees in two dimensions

Fast Fourier Method for the Valuation of Options on Several Correlated Currencies

The problem and notation

The method

Numerical results

Summary

Local Volatility Surfaces – Tackling the Smile

Introduction

The model

Introducing the smile into the model

The main steps on our way to price options

From implied volatility to the dispersion coefficient

Interpolation of the implied volatility

Pricing

Heston’s Stochastic Volatility Model Applied to Foreign Exchange Options

Introduction

Foreign exchange setting

Implementation

Partial differential equation for a general contingent claim

Calibration

Pricing one-touch options

Valuation of Options in Heston’s Stochastic Volatility Model Using Finite Element Methods

Introduction

Heston’s stochastic volatility model

Finite element method

Numerical solution

The basic idea of the finite element method

Selected solutions

A Jump Diffusion Model Applied to Foreign Exchange Markets

Introduction

A jump-diffusion model

Option pricing formula

Effect of parameters on the shape of the smile

Calibration to foreign exchange markets

Concluding remarks

A Model for Long Term Foreign Exchange Options

Introduction

The model

Vanilla option pricing

Implementation of the one-factor-model

Influence of correlation on the option price

Extension to multiple factors

Conclusions

Dealing with Dangerous Digitals

Introduction

Reverse up-and-out call

Model formulation and survey of super-replication under leverage constraints

Analytical solutions

Numerical Solutions

Summary

Testimonials

“The extent of the tools provided in the book is astonishingly broad and up-to-date... An excellent source for learning modern tools as well as market practices and conventions.“

Salih N. Neftci, Graduate School, CUNY

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