{"product_id":"foreign-exchange-option-pricing-9780470683682","title":"Foreign Exchange Option Pricing","description":"\u003cb\u003eBook Synopsis\u003c\/b\u003e\u003cbr\u003e*         This book covers foreign exchange options from the point of view of the finance practitioner.\u003cbr\u003e\u003cbr\u003e\u003cb\u003eTable of Contents\u003c\/b\u003e\u003cbr\u003e\u003cp\u003eAcknowledgements xiii\u003c\/p\u003e \u003cp\u003eList of Tables xv\u003c\/p\u003e \u003cp\u003eList of Figures xvii\u003c\/p\u003e \u003cp\u003e\u003cb\u003e1 Introduction 1\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e1.1 A Gentle Introduction to FX Markets 1\u003c\/p\u003e \u003cp\u003e1.2 Quotation Styles 2\u003c\/p\u003e \u003cp\u003e1.3 Risk Considerations 5\u003c\/p\u003e \u003cp\u003e1.4 Spot Settlement Rules 5\u003c\/p\u003e \u003cp\u003e1.5 Expiry and Delivery Rules 8\u003c\/p\u003e \u003cp\u003e1.5.1 Expiry and delivery rules – days or weeks 8\u003c\/p\u003e \u003cp\u003e1.5.2 Expiry and delivery rules – months or years 9\u003c\/p\u003e \u003cp\u003e1.6 Cutoff Times 10\u003c\/p\u003e \u003cp\u003e\u003cb\u003e2 Mathematical Preliminaries 13\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e2.1 The Black–Scholes Model 13\u003c\/p\u003e \u003cp\u003e2.1.1 Assumptions of the Black–Scholes model 13\u003c\/p\u003e \u003cp\u003e2.2 Risk Neutrality 13\u003c\/p\u003e \u003cp\u003e2.3 Derivation of the Black–Scholes equation 14\u003c\/p\u003e \u003cp\u003e2.3.1 Equity derivatives (without dividends) 14\u003c\/p\u003e \u003cp\u003e2.3.2 FX derivatives 15\u003c\/p\u003e \u003cp\u003e2.3.3 Terminal conditions and present value 17\u003c\/p\u003e \u003cp\u003e2.4 Integrating the SDE for S T 17\u003c\/p\u003e \u003cp\u003e2.5 Black–Scholes PDEs Expressed in Logspot 18\u003c\/p\u003e \u003cp\u003e2.6 Feynman–Kac and Risk-Neutral Expectation 18\u003c\/p\u003e \u003cp\u003e2.7 Risk Neutrality and the Presumption of Drift 20\u003c\/p\u003e \u003cp\u003e2.7.1 Equity derivatives (without dividends) 20\u003c\/p\u003e \u003cp\u003e2.7.2 FX derivatives – domestic risk-neutral measure 21\u003c\/p\u003e \u003cp\u003e2.7.3 FX derivatives – foreign risk-neutral measure 22\u003c\/p\u003e \u003cp\u003e2.8 Valuation of European Options 23\u003c\/p\u003e \u003cp\u003e2.8.1 Forward 26\u003c\/p\u003e \u003cp\u003e2.9 The Law of One Price 27\u003c\/p\u003e \u003cp\u003e2.10 The Black–Scholes Term Structure Model 28\u003c\/p\u003e \u003cp\u003e2.11 Breeden–Litzenberger Analysis 30\u003c\/p\u003e \u003cp\u003e2.12 European Digitals 31\u003c\/p\u003e \u003cp\u003e2.12.1 Static replication for bid\/offer digital pricing 32\u003c\/p\u003e \u003cp\u003e2.13 Settlement Adjustments 32\u003c\/p\u003e \u003cp\u003e2.14 Delayed Delivery Adjustments 33\u003c\/p\u003e \u003cp\u003e2.14.1 Delayed delivery adjustments – digitals 33\u003c\/p\u003e \u003cp\u003e2.14.2 Delayed delivery adjustments – Europeans 34\u003c\/p\u003e \u003cp\u003e2.15 Pricing using Fourier Methods 35\u003c\/p\u003e \u003cp\u003e2.15.1 European option pricing involving one numerical integral 37\u003c\/p\u003e \u003cp\u003e2.16 Leptokurtosis – More than Fat Tails 38\u003c\/p\u003e \u003cp\u003e\u003cb\u003e3 Deltas and Market Conventions 41\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e3.1 Quote Style Conversions 41\u003c\/p\u003e \u003cp\u003e3.2 The Law of Many Deltas 43\u003c\/p\u003e \u003cp\u003e3.2.1 Pips spot delta 44\u003c\/p\u003e \u003cp\u003e3.2.2 Percentage spot delta (premium adjusted) 45\u003c\/p\u003e \u003cp\u003e3.2.3 Pips forward delta 45\u003c\/p\u003e \u003cp\u003e3.2.4 Percentage forward delta (premium adjusted) 45\u003c\/p\u003e \u003cp\u003e3.2.5 Simple delta 45\u003c\/p\u003e \u003cp\u003e3.2.6 Equivalence between pips and percentage deltas 46\u003c\/p\u003e \u003cp\u003e3.2.7 Premium adjustment 46\u003c\/p\u003e \u003cp\u003e3.2.8 Summary 47\u003c\/p\u003e \u003cp\u003e3.3 FX Delta Conventions 47\u003c\/p\u003e \u003cp\u003e3.3.1 To premium adjust or not? 47\u003c\/p\u003e \u003cp\u003e3.3.2 Spot delta or forward delta? 48\u003c\/p\u003e \u003cp\u003e3.3.3 Notation 49\u003c\/p\u003e \u003cp\u003e3.4 Market Volatility Surfaces 49\u003c\/p\u003e \u003cp\u003e3.4.1 Sample market volatility surfaces 50\u003c\/p\u003e \u003cp\u003e3.5 At-the-Money 50\u003c\/p\u003e \u003cp\u003e3.5.1 At-the-money – ATMF 51\u003c\/p\u003e \u003cp\u003e3.5.2 At-the-money – DNS 51\u003c\/p\u003e \u003cp\u003e3.5.3 At-the-money strikes – summary 52\u003c\/p\u003e \u003cp\u003e3.5.4 Example – EURUSD 1Y 52\u003c\/p\u003e \u003cp\u003e3.5.5 Example – USDJPY 1Y 53\u003c\/p\u003e \u003cp\u003e3.6 Market Strangle 53\u003c\/p\u003e \u003cp\u003e3.6.1 Example – EURUSD 1Y 55\u003c\/p\u003e \u003cp\u003e3.7 Smile Strangle and Risk Reversal 55\u003c\/p\u003e \u003cp\u003e3.7.1 Smile strangle from market strangle – algorithm 56\u003c\/p\u003e \u003cp\u003e3.8 Visualisation of Strangles 57\u003c\/p\u003e \u003cp\u003e3.9 Smile Interpolation – Polynomial in Delta 59\u003c\/p\u003e \u003cp\u003e3.9.1 Example – EURUSD 1Y – polynomial in delta 59\u003c\/p\u003e \u003cp\u003e3.10 Smile Interpolation – SABR 60\u003c\/p\u003e \u003cp\u003e3.10.1 Example – EURUSD 1Y – SABR 61\u003c\/p\u003e \u003cp\u003e3.11 Concluding Remarks 62\u003c\/p\u003e \u003cp\u003e\u003cb\u003e4 Volatility Surface Construction 63\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e4.1 Volatility Backbone – Flat Forward Interpolation 65\u003c\/p\u003e \u003cp\u003e4.2 Volatility Surface Temporal Interpolation 67\u003c\/p\u003e \u003cp\u003e4.2.1 Volatility smile extrapolation 67\u003c\/p\u003e \u003cp\u003e4.2.2 Volatility smile interpolation 68\u003c\/p\u003e \u003cp\u003e4.2.3 Flat forward vol interpolation in smile strikes 69\u003c\/p\u003e \u003cp\u003e4.2.4 Example – EURUSD 18M from 1Y and 2Y tenors – SABR 70\u003c\/p\u003e \u003cp\u003e4.3 Volatility Surface Temporal Interpolation – Holidays and Weekends 70\u003c\/p\u003e \u003cp\u003e4.4 Volatility Surface Temporal Interpolation – Intraday Effects 73\u003c\/p\u003e \u003cp\u003e\u003cb\u003e5 Local Volatility and Implied Volatility 77\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e5.1 Introduction 77\u003c\/p\u003e \u003cp\u003e5.2 The Fokker–Planck Equation 78\u003c\/p\u003e \u003cp\u003e5.2.1 Derivation of the one-dimensional Fokker–Planck equation 79\u003c\/p\u003e \u003cp\u003e5.2.2 The multidimensional Fokker–Planck equation 82\u003c\/p\u003e \u003cp\u003e5.3 Dupire’s Construction of Local Volatility 83\u003c\/p\u003e \u003cp\u003e5.3.1 Dupire’s local volatility – the r\u003csup\u003ed\u003c\/sup\u003e = r\u003csup\u003ef \u003c\/sup\u003e= 0 case 84\u003c\/p\u003e \u003cp\u003e5.3.2 Dupire’s local volatility – with nonzero but constant interest rates 85\u003c\/p\u003e \u003cp\u003e5.4 Implied Volatility and Relationship to Local Volatility 86\u003c\/p\u003e \u003cp\u003e5.5 Local Volatility as Conditional Expectation 87\u003c\/p\u003e \u003cp\u003e5.6 Local Volatility for FX Markets 88\u003c\/p\u003e \u003cp\u003e5.7 Diffusion and PDE for Local Volatility 89\u003c\/p\u003e \u003cp\u003e5.8 The CEV Model 90\u003c\/p\u003e \u003cp\u003e5.8.1 Asymptotic expansion 91\u003c\/p\u003e \u003cp\u003e\u003cb\u003e6 Stochastic Volatility 95\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e6.1 Introduction 95\u003c\/p\u003e \u003cp\u003e6.2 Uncertain Volatility 95\u003c\/p\u003e \u003cp\u003e6.3 Stochastic Volatility Models 96\u003c\/p\u003e \u003cp\u003e6.3.1 The Heston model 98\u003c\/p\u003e \u003cp\u003e6.3.2 The Stein and Stein model 104\u003c\/p\u003e \u003cp\u003e6.3.3 Longstaff’s double square root model 105\u003c\/p\u003e \u003cp\u003e6.3.4 Scott’s exponential Ornstein–Uhlenbeck model 105\u003c\/p\u003e \u003cp\u003e6.3.5 The SABR model 106\u003c\/p\u003e \u003cp\u003e6.4 Uncorrelated Stochastic Volatility 107\u003c\/p\u003e \u003cp\u003e6.5 Stochastic Volatility Correlated with Spot 108\u003c\/p\u003e \u003cp\u003e6.6 The Fokker–Planck PDE Approach 111\u003c\/p\u003e \u003cp\u003e6.7 The Feynman–Kac PDE Approach 113\u003c\/p\u003e \u003cp\u003e6.7.1 Heston model – example 116\u003c\/p\u003e \u003cp\u003e6.7.2 Heston model – logspot coordinates 117\u003c\/p\u003e \u003cp\u003e6.8 Local Stochastic Volatility (LSV) Models 117\u003c\/p\u003e \u003cp\u003e6.8.1 Calibration of local volatility in LSV models 118\u003c\/p\u003e \u003cp\u003e6.8.2 Fokker–Planck equation for the LSV model 119\u003c\/p\u003e \u003cp\u003e6.8.3 Forward induction for local volatility calibration on LSV 120\u003c\/p\u003e \u003cp\u003e6.8.4 Calibrating stochastic and local volatilities 124\u003c\/p\u003e \u003cp\u003e6.8.5 The pricing PDE for LSV models 127\u003c\/p\u003e \u003cp\u003e\u003cb\u003e7 Numerical Methods for Pricing and Calibration 129\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e7.1 One-Dimensional Root Finding – Implied Volatility Calculation 129\u003c\/p\u003e \u003cp\u003e7.2 Nonlinear Least Squares Minimisation 130\u003c\/p\u003e \u003cp\u003e7.3 Monte Carlo Simulation 131\u003c\/p\u003e \u003cp\u003e7.3.1 Handling large timesteps with local volatility 134\u003c\/p\u003e \u003cp\u003e7.3.2 Monte Carlo convergence goes as 1\/√N 135\u003c\/p\u003e \u003cp\u003e7.3.3 Finding a balance between simulations and timesteps 138\u003c\/p\u003e \u003cp\u003e7.3.4 Quasi Monte Carlo convergence can be as good as 1\/N 142\u003c\/p\u003e \u003cp\u003e7.3.5 Variance reduction 143\u003c\/p\u003e \u003cp\u003e7.4 Convection–Diffusion PDEs in Finance 147\u003c\/p\u003e \u003cp\u003e7.4.1 Visualising diffusion 149\u003c\/p\u003e \u003cp\u003e7.4.2 Visualising convection 151\u003c\/p\u003e \u003cp\u003e7.5 Numerical Methods for PDEs 153\u003c\/p\u003e \u003cp\u003e7.6 Explicit Finite Difference Scheme 155\u003c\/p\u003e \u003cp\u003e7.6.1 Boundary conditions 157\u003c\/p\u003e \u003cp\u003e7.6.2 Von Neumann stability and the dimensionless heat equation 159\u003c\/p\u003e \u003cp\u003e7.7 Explicit Finite Difference on Nonuniform Meshes 163\u003c\/p\u003e \u003cp\u003e7.7.1 Mixed partial derivative terms on nonuniform meshes 165\u003c\/p\u003e \u003cp\u003e7.8 Implicit Finite Difference Scheme 165\u003c\/p\u003e \u003cp\u003e7.9 The Crank–Nicolson Scheme 167\u003c\/p\u003e \u003cp\u003e7.10 Numerical Schemes for Multidimensional PDEs 168\u003c\/p\u003e \u003cp\u003e7.10.1 Two-dimensional Crank–Nicolson scheme 169\u003c\/p\u003e \u003cp\u003e7.10.2 An early ADI scheme – Peaceman–Rachford splitting 169\u003c\/p\u003e \u003cp\u003e7.10.3 Douglas–Rachford splitting 171\u003c\/p\u003e \u003cp\u003e7.10.4 Craig–Sneyd splitting 172\u003c\/p\u003e \u003cp\u003e7.11 Practical Nonuniform Grid Generation Schemes 173\u003c\/p\u003e \u003cp\u003e7.11.1 Uniform grid generation 173\u003c\/p\u003e \u003cp\u003e7.11.2 Uniform grid generation with required levels 173\u003c\/p\u003e \u003cp\u003e7.11.3 Spatial grid generation 174\u003c\/p\u003e \u003cp\u003e7.11.4 Temporal grid generation 175\u003c\/p\u003e \u003cp\u003e7.12 Further Reading 176\u003c\/p\u003e \u003cp\u003e\u003cb\u003e8 First Generation Exotics – Binary and Barrier Options 177\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e8.1 The Reflection Principle 179\u003c\/p\u003e \u003cp\u003e8.2 European Barriers and Binaries 180\u003c\/p\u003e \u003cp\u003e8.2.1 European barriers 180\u003c\/p\u003e \u003cp\u003e8.2.2 Barrier parity relationships 182\u003c\/p\u003e \u003cp\u003e8.2.3 European digitals 183\u003c\/p\u003e \u003cp\u003e8.3 Continuously Monitored Binaries and Barriers 183\u003c\/p\u003e \u003cp\u003e8.3.1 Domestic binaries 188\u003c\/p\u003e \u003cp\u003e8.3.2 Foreign binaries 189\u003c\/p\u003e \u003cp\u003e8.3.3 Instant one-touch products 190\u003c\/p\u003e \u003cp\u003e8.3.4 Barrier products 191\u003c\/p\u003e \u003cp\u003e8.3.5 KIKOs and ONTOs 194\u003c\/p\u003e \u003cp\u003e8.4 Double Barrier Products 194\u003c\/p\u003e \u003cp\u003e8.5 Sensitivity to Local and Stochastic Volatility 195\u003c\/p\u003e \u003cp\u003e8.6 Barrier Bending 197\u003c\/p\u003e \u003cp\u003e8.7 Value Monitoring 202\u003c\/p\u003e \u003cp\u003e8.7.1 Compounds 202\u003c\/p\u003e \u003cp\u003e8.7.2 Americans 203\u003c\/p\u003e \u003cp\u003e8.7.3 Bermudans 203\u003c\/p\u003e \u003cp\u003e\u003cb\u003e9 Second Generation Exotics 205\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e9.1 Chooser Options 206\u003c\/p\u003e \u003cp\u003e9.2 Range Accrual Options 206\u003c\/p\u003e \u003cp\u003e9.3 Forward Start Options 207\u003c\/p\u003e \u003cp\u003e9.3.1 Strike reset options 209\u003c\/p\u003e \u003cp\u003e9.4 Lookback Options 209\u003c\/p\u003e \u003cp\u003e9.4.1 Double lookback options 211\u003c\/p\u003e \u003cp\u003e9.5 Asian Options 212\u003c\/p\u003e \u003cp\u003e9.5.1 Notes on seasoned Asians and fixing at expiry 214\u003c\/p\u003e \u003cp\u003e9.6 Target Redemption Notes 214\u003c\/p\u003e \u003cp\u003e9.7 Volatility and Variance Swaps 214\u003c\/p\u003e \u003cp\u003e9.7.1 Volatility observation 215\u003c\/p\u003e \u003cp\u003e9.7.2 Product specification and value at expiry 216\u003c\/p\u003e \u003cp\u003e9.7.3 Variance swap product valuation 217\u003c\/p\u003e \u003cp\u003e9.7.4 Volatility swap product valuation 219\u003c\/p\u003e \u003cp\u003e\u003cb\u003e10 Multicurrency Options 225\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e10.1 Correlations, Triangulation and Absence of Arbitrage 226\u003c\/p\u003e \u003cp\u003e10.2 Exchange Options 229\u003c\/p\u003e \u003cp\u003e10.3 Quantos 229\u003c\/p\u003e \u003cp\u003e10.3.1 Self-quanto option 230\u003c\/p\u003e \u003cp\u003e10.3.2 Self-quanto forward 231\u003c\/p\u003e \u003cp\u003e10.3.3 General quanto options 231\u003c\/p\u003e \u003cp\u003e10.4 Best-ofs and Worst-ofs 233\u003c\/p\u003e \u003cp\u003e10.4.1 Two-asset best-of call 234\u003c\/p\u003e \u003cp\u003e10.4.2 Three-asset best-of call 236\u003c\/p\u003e \u003cp\u003e10.4.3 N-asset best-of call 239\u003c\/p\u003e \u003cp\u003e10.5 Basket Options 239\u003c\/p\u003e \u003cp\u003e10.6 Numerical Methods 241\u003c\/p\u003e \u003cp\u003e10.7 A Note on Multicurrency Greeks 242\u003c\/p\u003e \u003cp\u003e10.8 Quantoing Untradeable Factors 243\u003c\/p\u003e \u003cp\u003e10.9 Further Reading 244\u003c\/p\u003e \u003cp\u003e\u003cb\u003e11 Longdated FX 245\u003c\/b\u003e\u003c\/p\u003e \u003cp\u003e11.1 Currency Swaps 245\u003c\/p\u003e \u003cp\u003e11.2 Basis Risk 247\u003c\/p\u003e \u003cp\u003e11.3 Forward Measure 249\u003c\/p\u003e \u003cp\u003e11.4 LIBOR in Arrears 250\u003c\/p\u003e \u003cp\u003e11.5 Typical Longdated FX Products 253\u003c\/p\u003e \u003cp\u003e11.5.1 Power reverse dual currency notes 253\u003c\/p\u003e \u003cp\u003e11.5.2 FX target redemption notes 254\u003c\/p\u003e \u003cp\u003e11.5.3 Effect on USDJPY volatility smile 255\u003c\/p\u003e \u003cp\u003e11.6 The Three-Factor Model 255\u003c\/p\u003e \u003cp\u003e11.7 Interest Rate Calibration of the Three-Factor Model 257\u003c\/p\u003e \u003cp\u003e11.7.1 Determination of drifts 257\u003c\/p\u003e \u003cp\u003e11.7.2 Determination of Hull–White volatilities 258\u003c\/p\u003e \u003cp\u003e11.8 Spot FX Calibration of the Three-Factor Model 259\u003c\/p\u003e \u003cp\u003e11.8.1 FX vanillas with lognormal spot FX 260\u003c\/p\u003e \u003cp\u003e11.8.2 FX vanillas with CEV local volatility 261\u003c\/p\u003e \u003cp\u003e11.8.3 FX vanillas with Dupire local volatility 262\u003c\/p\u003e \u003cp\u003e11.9 Conclusion 264\u003c\/p\u003e \u003cp\u003eReferences 265\u003c\/p\u003e \u003cp\u003eFurther Reading 271\u003c\/p\u003e \u003cp\u003eIndex 273\u003c\/p\u003e","brand":"John Wiley \u0026 Sons Inc","offers":[{"title":"Default Title","offer_id":49402409222487,"sku":"9780470683682","price":63.0,"currency_code":"GBP","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0817\/1739\/5799\/files\/9780470683682.jpg?v=1730480313","url":"https:\/\/bookcurl.com\/products\/foreign-exchange-option-pricing-9780470683682","provider":"Book Curl","version":"1.0","type":"link"}