Foreign Exchange Option Pricing: A Practitioners Guide / Edition 1

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This book covers foreign exchange options from the point of view ofthe finance practitioner. It contains everything a quant or traderworking in a bank or hedge fund would need to know about themathematics of foreign exchange—not just the theoreticalmathematics covered in other books but also comprehensive coverageof implementation, pricing and calibration.  

With content developed with input from traders and with examplesusing real-world data, this book introduces many of the morecommonly requested products from FX options trading desks, togetherwith the models that capture the risk characteristics necessary toprice these products accurately. Crucially, this book describes thenumerical methods required for calibration of these models –an area often neglected in the literature, which is nevertheless ofparamount importance in practice. Thorough treatment is given inone unified text to the following features:

  • Correct market conventions for FX volatility surfaceconstruction
  • Adjustment for settlement and delayed delivery of options
  • Pricing of vanillas and barrier options under the volatilitysmile
  • Barrier bending for limiting barrier discontinuity risk nearexpiry
  • Industry strength partial differential equations in one andseveral spatial variables using finite differences on nonuniformgrids
  • Fourier transform methods for pricing European options usingcharacteristic functions
  • Stochastic and local volatility models, and a mixedstochastic/local volatility model
  • Three-factor long-dated FX model
  • Numerical calibration techniques for all the models in thiswork
  • The augmented state variable approach for pricing stronglypath-dependent options using either partial differential equationsor Monte Carlo simulation

Connecting mathematically rigorous theory with practice, this isthe essential guide to foreign exchange options in the context ofthe real financial marketplace.

Table of Contents

Mathematical Preliminaries 

Deltas and Market Conventions

Volatility Surface Construction

Local Volatility and Implied Volatility

Stochastic Volatility

Numerical Methods for Pricing and Calibration

First Generation Exotics – Binary and Barrier Options

Second Generation Exotics

Multicurrency Options

Long-dated FX Options

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Product Details

  • ISBN-13: 9780470683682
  • Publisher: Wiley
  • Publication date: 2/2/2011
  • Series: Wiley Finance Series
  • Edition number: 1
  • Pages: 304
  • Product dimensions: 6.80 (w) x 9.70 (h) x 1.00 (d)

Table of Contents


List of Tables.

List of Figures.

1 Introduction.

1.1 A Gentle Introduction to FX Markets.

1.2 Quotation Styles.

1.3 Risk Considerations.

1.4 Spot Settlement Rules.

1.5 Expiry and Delivery Rules.

1.6 Cutoff Times.

2 Mathematical Preliminaries.

2.1 The Black–Scholes Model.

2.2 Risk Neutrality.

2.3 Derivation of the Black–Scholes equation.

2.4 Integrating the SDE for ST.

2.5 Black–Scholes PDEs Expressed in Logspot.

2.6 Feynman–Kac and Risk-Neutral Expectation.

2.7 Risk Neutrality and the Presumption of Drift.

2.8 Valuation of European Options.

2.9 The Law of One Price.

2.10 The Black–Scholes Term Structure Model.

2.11 Breeden–Litzenberger Analysis.

2.12 European Digitals.

2.13 Settlement Adjustments.

2.14 Delayed Delivery Adjustments.

2.15 Pricing using Fourier Methods.

2.16 Leptokurtosis – More than Fat Tails.

3 Deltas and Market Conventions.

3.1 Quote Style Conversions.

3.2 The Law of Many Deltas.

3.3 FX Delta Conventions.

3.4 Market Volatility Surfaces.

3.5 At-the-Money.

3.6 Market Strangle.

3.7 Smile Strangle and Risk Reversal.

3.8 Visualisation of Strangles.

3.9 Smile Interpolation – Polynomial in Delta.

3.10 Smile Interpolation – SABR.

3.11 Concluding Remarks.

4 Volatility Surface Construction.

4.1 Volatility Backbone – Flat Forward Interpolation.

4.2 Volatility Surface Temporal Interpolation.

4.3 Volatility Surface Temporal Interpolation – Holidaysand Weekends.

4.4 Volatility Surface Temporal Interpolation – IntradayEffects.

5 Local Volatility and Implied Volatility.

5.1 Introduction.

5.2 The Fokker–Planck Equation.

5.3 Dupire's Construction of Local Volatility.

5.4 Implied Volatility and Relationship to Local Volatility.

5.5 Local Volatility as Conditional Expectation.

5.6 Local Volatility for FX Markets.

5.7 Diffusion and PDE for Local Volatility.

5.8 The CEV Model.

6 Stochastic Volatility.

6.1 Introduction.

6.2 Uncertain Volatility.

6.3 Stochastic Volatility Models.

6.4 Uncorrelated Stochastic Volatility.

6.5 Stochastic Volatility Correlated with Spot.

6.6 The Fokker–Planck PDE Approach.

6.7 The Feynman–Kac PDE Approach.

6.8 Local Stochastic Volatility (LSV) Models.

7 Numerical Methods for Pricing and Calibration.

7.1 One-Dimensional Root Finding – Implied VolatilityCalculation.

7.2 Nonlinear Least Squares Minimisation.

7.3 Monte Carlo Simulation.

7.4 Convection–Diffusion PDEs in Finance.

7.5 Numerical Methods for PDEs.

7.6 Explicit Finite Difference Scheme.

7.7 Explicit Finite Difference on Nonuniform Meshes.

7.8 Implicit Finite Difference Scheme.

7.9 The Crank–Nicolson Scheme.

7.10 Numerical Schemes for Multidimensional PDEs.

7.11 Practical Nonuniform Grid Generation Schemes.

7.12 Further Reading.

8 First Generation Exotics – Binary and BarrierOptions.

8.1 The Reflection Principle.

8.2 European Barriers and Binaries.

8.3 Continuously Monitored Binaries and Barriers.

8.4 Double Barrier Products.

8.5 Sensitivity to Local and Stochastic Volatility.

8.6 Barrier Bending.

8.7 Value Monitoring.

9 Second Generation Exotics.

9.1 Chooser Options.

9.2 Range Accrual Options.

9.3 Forward Start Options.

9.4 Lookback Options.

9.5 Asian Options.

9.6 Target Redemption Notes.

9.7 Volatility and Variance Swaps.

10 Multicurrency Options.

10.1 Correlations, Triangulation and Absence of Arbitrage.

10.2 Exchange Options.

10.3 Quantos.

10.4 Best-ofs and Worst-ofs.

10.5 Basket Options.

10.6 Numerical Methods.

10.7 A Note on Multicurrency Greeks.

10.8 Quantoing Untradeable Factors.

10.9 Further Reading.

11 Longdated FX.

11.1 Currency Swaps.

11.2 Basis Risk.

11.3 Forward Measure.

11.4 LIBOR in Arrears.

11.5 Typical Longdated FX Products.

11.6 The Three-Factor Model.

11.7 Interest Rate Calibration of the Three-Factor Model.

11.8 Spot FX Calibration of the Three-Factor Model.

11.9 Conclusion.


Further Reading.


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