• 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

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