Dadachanji FX Barrier Options

A Comprehensive Guide for Industry Quants
1. Auflage 2015
ISBN: 978-1-137-46275-6
Verlag: Palgrave Macmillan UK
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, 274 Seiten

Reihe: Applied Quantitative Finance

This book is a quantitative quide to barrier options in FX environments.

Autoren/Hrsg.

Dadachanji, Zareer

Inhaltsverzeichnis

1;Cover;1
2;Half-Title;2
3;Tltle;4
4;Copyright;5
5;Dedication;6
6;Contents;8
7;List of Figures;13
8;List of Tables;20
9;Preface;21
10;Acknowledgements;25
11;Foreword;26
12;Glossary of Mathematical Notation;28
13;Contract Types;29
14;1 Meet the Products;31
14.1;1.1 Spot;31
14.1.1;1.1.1 Dollars per euro or euros per dollar?;33
14.1.2;1.1.2 Big figures and small figures;34
14.1.3;1.1.3 The value of Foreign;34
14.1.4;1.1.4 Converting between Domestic and Foreign;36
14.2;1.2 Forwards;36
14.2.1;1.2.1 The FX forward market;37
14.2.2;1.2.2 A formula for the forward rate;38
14.2.3;1.2.3 Payoff of a forward contract;40
14.2.4;1.2.4 Valuation of a forward contract;42
14.3;1.3 Vanilla options;42
14.3.1;1.3.1 Put–call parity;45
14.4;1.4 European digitals;46
14.5;1.5 Barrier-contingent vanilla options;46
14.6;1.6 Barrier-contingent payments;53
14.7;1.7 Rebates;55
14.8;1.8 Knock-in-knock-out (KIKO) options;55
14.9;1.9 Types of barriers;56
14.10;1.10 Structured products;57
14.11;1.11 Specifying the contract;58
14.12;1.12 Quantitative truisms;59
14.12.1;1.12.1 Foreign exchange symmetry and inversion;59
14.12.2;1.12.2 Knock-out plus knock-in equals no-barrier contract;59
14.12.3;1.12.3 Put–call parity;60
14.13;1.13 Jargon-buster;60
15;2 Living in a Black–Scholes World;63
15.1;2.1 The Black–Scholes model equation forspot price;63
15.2;2.2 The process for ln S;65
15.3;2.3 The Black–Scholes equation for option pricing;68
15.3.1;2.3.1 The lagless approach;68
15.3.2;2.3.2 Derivation of the Black–Scholes PDE;69
15.3.3;2.3.3 Black–Scholes model: hedging assumptions;72
15.3.4;2.3.4 Interpretation of the Black–Scholes PDE;73
15.4;2.4 Solving the Black–Scholes PDE;75
15.5;2.5 Payments;75
15.6;2.6 Forwards;77
15.7;2.7 Vanilla options;77
15.7.1;2.7.1 Transformation of the Black–Scholes PDE;78
15.7.2;2.7.2 Solution of the diffusion equation for vanilla options;82
15.7.3;2.7.3 The vanilla option pricing formulae;87
15.7.4;2.7.4 Price quotation styles;89
15.7.5;2.7.5 Valuation behaviour of vanilla options;90
15.8;2.8 Black–Scholes pricing of barrier-contingent vanilla options;94
15.8.1;2.8.1 Knock-outs;95
15.8.2;2.8.2 Knock-ins;99
15.8.3;2.8.3 Quotation methods;100
15.8.4;2.8.4 Valuation behaviour of barrier-contingent vanilla options;100
15.9;2.9 Black–Scholes pricing of barrier-contingent payments;103
15.9.1;2.9.1 Payment in Domestic;104
15.9.2;2.9.2 Payment in Foreign;106
15.9.3;2.9.3 Quotation methods;106
15.9.4;2.9.4 Valuation behaviour of barrier-contingent payments;107
15.10;2.10 Discrete barrier options;110
15.11;2.11 Window barrier options;110
15.12;2.12 Black–Scholes numerical valuation methods;111
16;3 Black–Scholes Risk Management;112
16.1;3.1 Spot risk;113
16.1.1;3.1.1 Local spot risk analysis;113
16.1.2;3.1.2 Delta;114
16.1.3;3.1.3 Gamma;115
16.1.4;3.1.4 Results for spot Greeks;116
16.1.5;3.1.5 Non-local spot risk analysis;127
16.2;3.2 Volatility risk;127
16.2.1;3.2.1 Local volatility risk analysis;128
16.2.2;3.2.2 Non-local volatility risk;142
16.3;3.3 Interest rate risk;143
16.4;3.4 Theta;145
16.5;3.5 Barrier over-hedging;147
16.6;3.6 Co-Greeks;150
17;4 Smile Pricing;151
17.1;4.1 The shortcomings of the Black–Scholes model;151
17.2;4.2 Black–Scholes with term structure (BSTS);153
17.3;4.3 The implied volatility surface;155
17.4;4.4 The FX vanilla option market;156
17.4.1;4.4.1 At-the-money volatility;159
17.4.2;4.4.2 Risk reversal;161
17.4.3;4.4.3 Butterfly;162
17.4.4;4.4.4 The role of the Black–Scholes model in the FX vanilla options market;163
17.5;4.5 Theoretical Value (TV);163
17.5.1;4.5.1 Conventions for extracting market data for TV calculations;164
17.5.2;4.5.2 Example broker quote request;165
17.6;4.6 Modelling market implied volatilities;166
17.7;4.7 The probability density function;167
17.8;4.8 Three things we want from a model;171
17.9;4.9 The local volatility (LV) model;171
17.9.1;4.9.1 It’s the smile dynamics, stupid;185
17.10;4.10 Five things we want from a model;186
17.11;4.11 Stochastic volatility (SV) models;187
17.11.1;4.11.1 SABR model;187
17.11.2;4.11.2 Heston model;188
17.12;4.12 Mixed local/stochastic volatility (LSV) models;192
17.12.1;4.12.1 Term structure of volatility of volatility;200
17.13;4.13 Other models and methods;201
17.13.1;4.13.1 Uncertain volatility (UV) models;201
17.13.2;4.13.2 Jump–diffusion models;202
17.13.3;4.13.3 Vanna–volga methods;203
18;5 Smile Risk Management;205
18.1;5.1 Black–Scholes with term structure;205
18.2;5.2 Local volatility model;209
18.3;5.3 Spot risk under smile models;210
18.4;5.4 Theta risk under smile models;212
18.5;5.5 Mixed local/stochastic volatility models;212
18.6;5.6 Static hedging;213
18.7;5.7 Managing risk across businesses;214
19;6 Numerical Methods;216
19.1;6.1 Finite-difference (FD) methods;216
19.1.1;6.1.1 Grid geometry;217
19.1.2;6.1.2 Finite-difference schemes;219
19.2;6.2 Monte Carlo (MC) methods;223
19.2.1;6.2.1 Monte Carlo schedules;224
19.2.2;6.2.2 Monte Carlo algorithms;225
19.2.3;6.2.3 Variance reduction;227
19.2.4;6.2.4 The Brownian Bridge;229
19.2.5;6.2.5 Early termination;230
19.3;6.3 Calculating Greeks;230
19.3.1;6.3.1 Bumped Greeks;230
19.3.2;6.3.2 Greeks from finite-difference calculations;232
19.3.3;6.3.3 Greeks from Monte Carlo;233
20;7 Further Topics;235
20.1;7.1 Managed currencies;235
20.2;7.2 Stochastic interest rates (SIR);236
20.3;7.3 Real-world pricing;240
20.3.1;7.3.1 Bid–offer spreads;240
20.3.2;7.3.2 Rules-based pricing methods;242
20.4;7.4 Regulation and market abuse;243
21;A Derivation of the Black–Scholes Pricing Equations for Vanilla Options;245
22;B Normal and Lognormal Probability Distributions;250
22.1;B.1 Normal distribution;250
22.2;B.2 Lognormal distribution;250
23;C Derivation of the Local Volatility Function;251
23.1;C.1 Derivation in terms of call prices;251
23.2;C.2 Local volatility from implied volatility;255
23.3;C.3 Working in moneyness space;257
23.4;C.4 Working in log space;258
23.5;C.5 Specialization to BSTS;259
24;D Calibration of Mixed Local/Stochastic Volatility (LSV) Models;260
25;E Derivation of Fokker–Planck Equation for the Local Volatility Model;262
26;Bibliography;264
27;Index;267