Foreign Exchange Risk: Models, Instruments and Strategies

  • ID: 220081
  • Book
  • 320 Pages
  • Incisive Media
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This book provides all the vital quantitative tools for foreign exchange options in a clear and logical manner

- 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
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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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