Foreign Exchange Risk: Models, Instruments and Strategies

Abstract

Preface Part I. Market: Products and Basics 1. Vanilla Options 1.1 Model and payoff 1.2 Value 1.3 Greeks 1.4 Identities 1.5 Quotation 1.6 Dual Black-Scholes partial differential equation 1.7 Retrieving the arguments 1.8 Greeks in terms of deltas 2. Volatility Management 2.1 Market risk of foreign exchange options 2.2 Historic volatility vs implied volatility 2.3 Market data 2.4 Volatility smile 2.5 Risk reversals and butterflies 2.6 Shape of the smile 2.7 Reasons for the smile 2.8 Term structure models and formulae 2.9 Wing shifts 2.10 Term structure of volatility at-the-money 3. Handling Differing Expiry and Delivery Dates 4. The Impact of Non-business Days on the Pricing of Options 4.1 Introduction 4.2 Model and results 5. Barrier Options - An Overview 5.1 What is a barrier option? 5.2 The popularity of barrier options 5.3 Barrier option crisis in 1994-96, questions about exotics in general 5.4 Types of barriers 5.5 How the barrier is monitored (continuous vs discrete) and how this influences the price 5.6 How breaching the barrier is determined 5.7 Hedging methods, coping with high delta and gamma 5.8 How large barrier contracts affect the market 5.9 Difference between market prices and theoretical Black-Scholes values explained 6. The Pricing of First Generation Exotics 6.1 Introduction 6.2 Single barrier options 6.3 Digital options 6.4 One-touch options 6.5 Double no-touch options 6.6 Corridors 6.7 Double barrier options 6.8 Fade-in-out options 7. The Pricing of Second Generation Exotics 7.1 Introduction 7.2 Forward-start options 7.3 Ratchet options 7.4 Power options 7.5 Installment options 7.6 Stairs options 7.7 Compound on forward start strategy 7.8 Options on the minimum/maximum 7.9 Generalized options on the minimum/maximum 8. Quanto Options 8.1 Introduction 8.2 Quanto forward 8.3 Quanto European plain vanilla 8.4 Quanto forward start plain vanilla 8.5 Quanto power option 9.No-Arbitrage Bounds and Static Hedging of Compound Options 9.1 Compound options 9.2 Put-call parity and no-arbitrage bounds for compound options 9.3 Value of compound options in the Black-Scholes model 9.4 Hedging of compound options 9.5 Static hedging of compound options 10.Taking a Corporate View: Zero Cost Structures 10.1 Products and markets 10.2 Pricing 10.3 Conclusion 11.Probability Density Functions and Related Tools 11.1 Motivation 11.2 The probability density function 11.3 First exit times 12. A Note on Forward and Backward Partial Differential Equations for Derivative Contracts with Forwards as Underlyings 12.1 Introduction 12.2 Forward and backward equations 12.3 Forward-based derivation of backward and forward partial differential equations 12.4 Summary Part II. Risk Management 13. Efficient Computation of Option Price Sensitivities Using Homogeneity and Other Tricks 13.1 Introduction 13.2 Fundamental properties 13.3 European options in the Black-Scholes model 13.4 The one-dimensional case 13.5 A European claim in the two-dimensional Black-Scholes model 13.6 Summary 14. How the Greeks Would Have Hedged Correlation Risk of Foreign Exchange Options 14.1 Introduction 14.2 Foreign exchange market model 14.3 The extension beyond triangular markets 14.4 Geometric interpretation 14.5 Hedging correlation risk Part III. Models and Applications to Exotic Options 15. An Arithmetic Average Model with Applications to Pricing Asian and Basket Options 15.1 Introduction 15.2 Moment matching for the arithmetic spot 15.3 Alternative method of pricing using stochastic Taylor expansion 15.4 Asian options 15.5 Basket options 15.6 Conclusion 16. Finite Differences 16.1 Introduction 16.2 Black-Scholes framework 16.3 Stochastic volatility models 16.4 Path dependence at discrete points in time 16.5 The Greeks 17. Monte Carlo Simulations and Variance Reduction Techniques 17.1 Introduction 17.2 The method 17.3 Path-independent derivatives 17.4 Variance reduction methods 17.5 Barrier options 17.6 Stochastic volatility 17.7 Calculating the Greeks 18. Quasi-Random Numbers and their Application to Pricing Basket and Lookback Options 18.1 Introduction 18.2 Some quasi-random sequences and a qualitative description 18.3 The discrepancy, a quantitative description 18.4 Independent quasi-random numbers 18.5 Examples of Monte Carlo integration with quasi-random numbers 18.6 Convergence 18.7 Basket options 18.8 Lookback options 18.9 Conclusion 19. Quasi-Monte Carlo Techniques for the Valuation of Contingent Claims on Several Assets 19.1 Introduction 19.2 Problem and notation 19.3 The methods 19.4 Numerical results 19.5 Summary 20. Binomial Trees in One and Two Dimensions 20.1 One step model 20.2 The martingale measure 20.3 Implementation 20.4 Convergence 20.5 Barrier options 20.6 Binomial trees in two dimensions 21. Fast Fourier Method for the Valuation of Options on Several Correlated Currencies 21.1 The problem and notation 21.2 The method 21.3 Numerical results 21.4 Summary 22. Local Volatility Surfaces - Tackling the Smile 22.1 Introduction 22.2 The model 22.3 Introducing the smile into the model 22.4 The main steps on our way to price options 22.5 From implied volatility to the dispersion coefficient 22.6 Interpolation of the implied volatility 22.7 Pricing 23. Heston's Stochastic Volatility Model Applied to Foreign Exchange Options 23.1 Introduction 23.2 Foreign exchange setting 23.3 Implementation 23.4 Partial differential equation for a general contingent claim 23.5 Calibration 23.6 Pricing one-touch options 24. Valuation of Options in Heston's Stochastic Volatility Model Using Finite Element Methods 24.1 Introduction 24.2 Heston's stochastic volatility model 24.3 Finite element method 24.4 Numerical solution 24.5 The basic idea of the finite element method 24.6 Selected solutions 25. A Jump Diffusion Model Applied to Foreign Exchange Markets 25.1 Introduction 25.2 A jump-diffusion model 25.3 Option pricing formula 25.4 Effect of parameters on the shape of the smile 25.5 Calibration to foreign exchange markets 25.6 Concluding remarks 26. A Model for Long Term Foreign Exchange Options 26.1 Introduction 26.2 The model 26.3 Vanilla option pricing 26.4 Implementation of the one-factor-model 26.5 Influence of correlation on the option price 26.6 Extension to multiple factors 26.7 Conclusions 27. Dealing with Dangerous Digitals 27.1 Introduction 27.2 Reverse up-and-out call 27.3 Model formulation and survey of super-replication under leverage constraints 27.4 Analytical solutions 27.5 Numerical Solutions 27.6 Summary Index

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