FX Barrier Options

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.

'FX Barrier Options are the subject of more in-depth study by practitioners than almost any other class of exotic options and yet they have been given relatively short shrift in the literature until now. Zareer Dadachanji's book brilliantly fills this gap. Readers are led gently but thoroughly from the basics to the state of the art with ample discussion throughout (and full mathematical details supplied in appendices). Highly recommended for beginners and experts alike.'

Ben Nasatyr, Head of FX Quantitative Analysis, Citigroup

'Zareer Dadachanji's book on FX barrier options is clear, precise, and a pleasure to read. The derivations are as simple as possible while remaining correct, and the book displays a judicious blend of theory, modelling and practice. Students and practitioners will learn a lot (and not just about FX barrier options), and will do so with pleasure.'

Riccardo Rebonato, Global Head of Rates and FX Analytics, PIMCO, and Visiting Lecturer, Mathematical Finance, Oxford University

'The market in FX barrier options has grown from a niche to the most liquid exotics market in the world, requiring models that are both very sophisticated and computationally efficient. The first of its kind, Dr Dadachanji's treatise is exclusively dedicated to the subject. The book requires few prerequisites but quickly builds to the state of the art in a clear and comprehensive manner. Undoubtedly it will be an indispensable companion to anyone involved in the subject or interested in learning it.'

Vladimir Piterbarg, Head of Quantitative Analytics at Rokos Family Office

'This is the book I wish I'd had when I started my career as an FX quant an insider's view of FX barrier option modelling from both a theoretical and practical perspective. It builds from the basic market set-up through to the latest techniques in an FX quant's toolkit.'

Mark Jex, FX Quant in investment banks for 20 years, and pioneer of the mixed local/ stochastic volatility model

'As one who understands financial engineering from the trader's perspective as well as from the quant's, Zareer Dadachanji has written a very valuable book on FX barrier options. Requiring very little pre-requisite financial knowledge, it guides readers through the plethora of quantitative concepts, techniques and practical issues associated with these products. And it is an enjoyable read to boot.'

Simon Hards, Global Head of FX Trading at Credit Suisse

Auteur
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.

Contenu

Preface Foreword Glossary of Mathematical Notation Contract Types 1 Meet the Products 1.1 Spot 1.1.1 Dollars per euro or euros per dollar? 1.1.2 Big figures and small figures 1.1.3 The value of Foreign 1.1.4 Converting between Domestic and Foreign 1.2 Forwards 1.2.1 The FX forward market 1.2.2 A formula for the forward rate 1.2.3 Payoff a forward contract 1.2.4 Valuation of a forward contract 1.3 Vanilla options 1.3.1 Put-Call Parity 1.4 Barrier-contingent vanilla options 1.5 Barrier-contingent payments 1.6 Rebates 1.7 Knock-in-knock-out (KIKO) options 1.8 Types of barriers 1.9 Structured products 1.10 Specifying the contract 1.11 Quantitative truisms 1.11.1 Foreign exchange symmetry and inversion 1.11.2 Knock-out plus knock-in equals no-barrier contract 1.11.3 Put-call parity 1.12 Jargon-buster 2 Living in a Black-Scholes World 2.1 The Black-Scholes model equation for spot price 2.2 The process for ln S 2.3 The Black-Scholes equation for option pricing 2.3.1 The lagless approach 2.3.2 Derivation of the Black-Scholes PDE 2.3.3 Black-Scholes model | hedging assumptions 2.3.4 Interpretation of the Black-Scholes PDE 2.4 Solving the Black-Scholes PDE 2.5 Payments 2.6 Forwards 2.7 Vanilla options 2.7.1 Transformation of the Black-Scholes PDE 2.7.2 Solution of the diffusion equation for vanilla options 2.7.3 The vanilla option pricing formulae 2.7.4 Price quotation styles 2.7.5 Valuation behaviour 2.8 Black-Scholes pricing of barrier-contingent vanilla options 2.8.1 Knock-outs 2.8.2 Knock-ins 2.8.3 Quotation methods 2.8.4 Valuation behaviour 2.9 Black-Scholes pricing of barrier-contingent payments 2.9.1 Payment in Domestic 2.9.2 Payment in Foreign 2.9.3 Quotation methods 2.9.4 Valuation behaviour 2.10 Discrete barrier options 2.11 Window barrier options 2.12 Black-Scholes numerical valuation methods 3 Black-Scholes Risk Management 3.1 Spot risk 3.1.1 Local spot risk analysis 3.1.2 Delta 3.1.3 Gamma 3.1.4 Results for spot Greeks 3.1.5 Non-local spot risk analysis 3.2 Volatility risk 3.2.1 Local volatility risk analysis 3.2.2 Non-local volatility risk 3.3 Interest rate risk 3.4 Theta 3.5 Barrier over-hedging 3.6 Co-Greeks 4 Smile Pricing 4.1 The shortcomings of the Black-Scholes model 4.2 Black-Scholes with term structure (BSTS) 4.3 The implied volatility surface 4.4 The FX vanilla option market 4.4.1 At-the-money volatility 4.4.2 Risk reversal 4.4.3 Buttery 4.4.4 The role of the Black-Scholes model in the FX vanilla options market 4.5 Theoretical Value (TV) 4.5.1 Conventions for extracting market data for TV calculations 4.5.2 Example broker quote request 4.6 Modelling market implied volatilities 4.7 The probability density function 4.8 Three things we wan…