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, eBook

Reihe: Applied Quantitative Finance

Barrier options are a class of highly path-dependent exotic options which present particular challenges to practitioners in all areas of the financial industry. They are traded heavily as stand-alone contracts in the Foreign Exchange (FX) options market, their trading volume being second only to that of vanilla options. The FX options industry has correspondingly shown great innovation in this class of products and in the models that are used to value and risk-manage them.

FX structured products commonly include barrier features, and in order to analyse the effects that these features have on the overall structured product, it is essential first to understand how individual barrier options work and behave.
FX Barrier Options takes a quantitative approach to barrier options in FX environments. Its primary perspectives are those of quantitative analysts, both in the front office and in control functions. It presents and explains concepts in a highly intuitive manner throughout, to allow quantitatively minded traders, structurers, marketers, salespeople and software engineers to acquire a more rigorous analytical understanding of these products.

The book derives, demonstrates and analyses a wide range of models, modelling techniques and numerical algorithms that can be used for constructing valuation models and risk-management methods. Discussions focus on the practical realities of the market and demonstrate the behaviour of models based on real and recent market data across a range of currency pairs. It furthermore offers a clear description of the history and evolution of the different types of barrier options, and elucidates a great deal of industry nomenclature and jargon.

Zielgruppe

Research

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

Über Autor(innen)

Zareer Dadachanji is a quantitative analysis consultant with nearly two decades of corporate experience, mostly in financial quantitative modelling across a range of asset classes. He has spent 14 years working as a front-office quant at banks and hedge funds, including NatWest/RBS, Credit Suisse and latterly Standard Chartered Bank, where he held the position of Global Head of FX Quants. Zareer's specialist areas of expertise are the modelling of FX and equity derivatives. He combines these specialist areas with substantial knowledge of general quantitative modelling, gained through years of senior-level engagement in the activities of global cross-asset quant teams. Zareer is the founder and director of Model Quant Solutions, an independent consultancy providing bespoke quantitative analysis and training on a range of financial subjects. The consultancy serves a variety of clients and client types across the finance industry. Zareer holds a triple first in Natural Sciences and a PhD in Computational and Theoretical Physics, both from the University of Cambridge.