Foreign Exchange Option Pricing : A Practitioners Guide.
Title:
Foreign Exchange Option Pricing : A Practitioners Guide.
Author:
Clark, Iain J.
ISBN:
9780470977194
Personal Author:
Edition:
1st ed.
Physical Description:
1 online resource (300 pages)
Series:
The Wiley Finance Series ; v.602
The Wiley Finance Series
Contents:
Foreign Exchange Option Pricing -- Contents -- Acknowledgements -- 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 -- 1.5.1 Expiry and delivery rules - days or weeks -- 1.5.2 Expiry and delivery rules - months or years -- 1.6 Cutoff Times -- 2 Mathematical Preliminaries -- 2.1 The Black-Scholes Model -- 2.1.1 Assumptions of the Black-Scholes model -- 2.2 Risk Neutrality -- 2.3 Derivation of the Black-Scholes equation -- 2.3.1 Equity derivatives (without dividends) -- 2.3.2 FX derivatives -- 2.3.3 Terminal conditions and present value -- 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 -- 2.7.1 Equity derivatives (without dividends) -- 2.7.2 FX derivatives - domestic risk-neutral measure -- 2.7.3 FX derivatives - foreign risk-neutral measure -- 2.8 Valuation of European Options -- 2.8.1 Forward -- 2.9 The Law of One Price -- 2.10 The Black-Scholes Term Structure Model -- 2.11 Breeden-Litzenberger Analysis -- 2.12 European Digitals -- 2.12.1 Static replication for bid/offer digital pricing -- 2.13 Settlement Adjustments -- 2.14 Delayed Delivery Adjustments -- 2.14.1 Delayed delivery adjustments - digitals -- 2.14.2 Delayed delivery adjustments - Europeans -- 2.15 Pricing using Fourier Methods -- 2.15.1 European option pricing involving one numerical integral -- 2.16 Leptokurtosis - More than Fat Tails -- 3 Deltas and Market Conventions -- 3.1 Quote Style Conversions -- 3.2 The Law of Many Deltas -- 3.2.1 Pips spot delta -- 3.2.2 Percentage spot delta (premium adjusted) -- 3.2.3 Pips forward delta -- 3.2.4 Percentage forward delta (premium adjusted).
3.2.5 Simple delta -- 3.2.6 Equivalence between pips and percentage deltas -- 3.2.7 Premium adjustment -- 3.2.8 Summary -- 3.3 FX Delta Conventions -- 3.3.1 To premium adjust or not? -- 3.3.2 Spot delta or forward delta? -- 3.3.3 Notation -- 3.4 Market Volatility Surfaces -- 3.4.1 Sample market volatility surfaces -- 3.5 At-the-Money -- 3.5.1 At-the-money - ATMF -- 3.5.2 At-the-money - DNS -- 3.5.3 At-the-money strikes - summary -- 3.5.4 Example - EURUSD 1Y -- 3.5.5 Example - USDJPY 1Y -- 3.6 Market Strangle -- 3.6.1 Example - EURUSD 1Y -- 3.7 Smile Strangle and Risk Reversal -- 3.7.1 Smile strangle from market strangle - algorithm -- 3.8 Visualisation of Strangles -- 3.9 Smile Interpolation - Polynomial in Delta -- 3.9.1 Example - EURUSD 1Y - polynomial in delta -- 3.10 Smile Interpolation - SABR -- 3.10.1 Example - EURUSD 1Y - SABR -- 3.11 Concluding Remarks -- 4 Volatility Surface Construction -- 4.1 Volatility Backbone - Flat Forward Interpolation -- 4.2 Volatility Surface Temporal Interpolation -- 4.2.1 Volatility smile extrapolation -- 4.2.2 Volatility smile interpolation -- 4.2.3 Flat forward vol interpolation in smile strikes -- 4.2.4 Example - EURUSD 18M from 1Y and 2Y tenors - SABR -- 4.3 Volatility Surface Temporal Interpolation - Holidays and Weekends -- 4.4 Volatility Surface Temporal Interpolation - Intraday Effects -- 5 Local Volatility and Implied Volatility -- 5.1 Introduction -- 5.2 The Fokker-Planck Equation -- 5.2.1 Derivation of the one-dimensional Fokker-Planck equation -- 5.2.2 The multidimensional Fokker-Planck equation -- 5.3 Dupire's Construction of Local Volatility -- 5.3.1 Dupire's local volatility - the r d = r f = 0 case -- 5.3.2 Dupire's local volatility - with nonzero but constant interest rates -- 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 -- 5.8.1 Asymptotic expansion -- 6 Stochastic Volatility -- 6.1 Introduction -- 6.2 Uncertain Volatility -- 6.3 Stochastic Volatility Models -- 6.3.1 The Heston model -- 6.3.2 The Stein and Stein model -- 6.3.3 Longstaff's double square root model -- 6.3.4 Scott's exponential Ornstein-Uhlenbeck model -- 6.3.5 The SABR model -- 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 -- 6.7.1 Heston model - example -- 6.7.2 Heston model - logspot coordinates -- 6.8 Local Stochastic Volatility (LSV) Models -- 6.8.1 Calibration of local volatility in LSV models -- 6.8.2 Fokker-Planck equation for the LSV model -- 6.8.3 Forward induction for local volatility calibration on LSV -- 6.8.4 Calibrating stochastic and local volatilities -- 6.8.5 The pricing PDE for LSV models -- 7 Numerical Methods for Pricing and Calibration -- 7.1 One-Dimensional Root Finding - Implied Volatility Calculation -- 7.2 Nonlinear Least Squares Minimisation -- 7.3 Monte Carlo Simulation -- 7.3.1 Handling large timesteps with local volatility -- 7.3.2 Monte Carlo convergence goes as 1/ N -- 7.3.3 Finding a balance between simulations and timesteps -- 7.3.4 Quasi Monte Carlo convergence can be as good as 1/N -- 7.3.5 Variance reduction -- 7.4 Convection-Diffusion PDEs in Finance -- 7.4.1 Visualising diffusion -- 7.4.2 Visualising convection -- 7.5 Numerical Methods for PDEs -- 7.6 Explicit Finite Difference Scheme -- 7.6.1 Boundary conditions -- 7.6.2 Von Neumann stability and the dimensionless heat equation -- 7.7 Explicit Finite Difference on Nonuniform Meshes -- 7.7.1 Mixed partial derivative terms on nonuniform meshes -- 7.8 Implicit Finite Difference Scheme.
7.9 The Crank-Nicolson Scheme -- 7.10 Numerical Schemes for Multidimensional PDEs -- 7.10.1 Two-dimensional Crank-Nicolson scheme -- 7.10.2 An early ADI scheme - Peaceman-Rachford splitting -- 7.10.3 Douglas-Rachford splitting -- 7.10.4 Craig-Sneyd splitting -- 7.11 Practical Nonuniform Grid Generation Schemes -- 7.11.1 Uniform grid generation -- 7.11.2 Uniform grid generation with required levels -- 7.11.3 Spatial grid generation -- 7.11.4 Temporal grid generation -- 7.12 Further Reading -- 8 First Generation Exotics - Binary and Barrier Options -- 8.1 The Reflection Principle -- 8.2 European Barriers and Binaries -- 8.2.1 European barriers -- 8.2.2 Barrier parity relationships -- 8.2.3 European digitals -- 8.3 Continuously Monitored Binaries and Barriers -- 8.3.1 Domestic binaries -- 8.3.2 Foreign binaries -- 8.3.3 Instant one-touch products -- 8.3.4 Barrier products -- 8.3.5 KIKOs and ONTOs -- 8.4 Double Barrier Products -- 8.5 Sensitivity to Local and Stochastic Volatility -- 8.6 Barrier Bending -- 8.7 Value Monitoring -- 8.7.1 Compounds -- 8.7.2 Americans -- 8.7.3 Bermudans -- 9 Second Generation Exotics -- 9.1 Chooser Options -- 9.2 Range Accrual Options -- 9.3 Forward Start Options -- 9.3.1 Strike reset options -- 9.4 Lookback Options -- 9.4.1 Double lookback options -- 9.5 Asian Options -- 9.5.1 Notes on seasoned Asians and fixing at expiry -- 9.6 Target Redemption Notes -- 9.7 Volatility and Variance Swaps -- 9.7.1 Volatility observation -- 9.7.2 Product specification and value at expiry -- 9.7.3 Variance swap product valuation -- 9.7.4 Volatility swap product valuation -- 10 Multicurrency Options -- 10.1 Correlations, Triangulation and Absence of Arbitrage -- 10.2 Exchange Options -- 10.3 Quantos -- 10.3.1 Self-quanto option -- 10.3.2 Self-quanto forward -- 10.3.3 General quanto options -- 10.4 Best-ofs and Worst-ofs.
10.4.1 Two-asset best-of call -- 10.4.2 Three-asset best-of call -- 10.4.3 N-asset best-of call -- 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 -- 11.5.1 Power reverse dual currency notes -- 11.5.2 FX target redemption notes -- 11.5.3 Effect on USDJPY volatility smile -- 11.6 The Three-Factor Model -- 11.7 Interest Rate Calibration of the Three-Factor Model -- 11.7.1 Determination of drifts -- 11.7.2 Determination of Hull-White volatilities -- 11.8 Spot FX Calibration of the Three-Factor Model -- 11.8.1 FX vanillas with lognormal spot FX -- 11.8.2 FX vanillas with CEV local volatility -- 11.8.3 FX vanillas with Dupire local volatility -- 11.9 Conclusion -- References -- Further Reading -- Index.
Abstract:
This book covers foreign exchange options from the point of view of the finance practitioner. It contains everything a quant or trader working in a bank or hedge fund would need to know about the mathematics of foreign exchange-not just the theoretical mathematics covered in other books but also comprehensive coverage of implementation, pricing and calibration. With content developed with input from traders and with examples using real-world data, this book introduces many of the more commonly requested products from FX options trading desks, together with the models that capture the risk characteristics necessary to price these products accurately. Crucially, this book describes the numerical methods required for calibration of these models - an area often neglected in the literature, which is nevertheless of paramount importance in practice. Thorough treatment is given in one unified text to the following features: Correct market conventions for FX volatility surface construction Adjustment for settlement and delayed delivery of options Pricing of vanillas and barrier options under the volatility smile Barrier bending for limiting barrier discontinuity risk near expiry Industry strength partial differential equations in one and several spatial variables using finite differences on nonuniform grids Fourier transform methods for pricing European options using characteristic functions Stochastic and local volatility models, and a mixed stochastic/local volatility model Three-factor long-dated FX model Numerical calibration techniques for all the models in this work The augmented state variable approach for pricing strongly path-dependent options using either partial differential equations or Monte Carlo simulation Connecting mathematically rigorous theory with practice, this is the essential guide to foreign exchange options in the context
of the 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.
Local Note:
Electronic reproduction. Ann Arbor, Michigan : ProQuest Ebook Central, 2017. Available via World Wide Web. Access may be limited to ProQuest Ebook Central affiliated libraries.
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Electronic Access:
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