Foreign-Exchange-Risk-Pricing-and-Hedging-Exotic-Instruments

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Foreign Exchange Risk: Pricing and Hedging Exotic Instruments

Foreign Exchange Risk: Pricing and Hedging Exotic Instruments Delia Pirnog1
Master of Advanced Studies in Finance Eidgen¨ssische Technische Hochschule / Universit¨t Z¨rich, o a u Schweiz Abstract This project discusses exotic instruments used in the Foreign Exchange(FX) markets. An overview of the most popular exotic derivatives is presented, followed by the pricing alternatives of these securities. Hedging methods using static replication for some classes of exotic options are afterward discussed. Finally, risk management control of an active FX portfolio is studied.

keywords: FX market, Exotic options, Option pricing, Barrier Options, Digital Options, Static Hedging, Dynamic Hedging. 1

Email: delia pirnog@yahoo.com

Acknowledgment This paper was sponsored by UBS as part of an internship at Market Risk Control department from UBS Opfikon. I would like to thank Professor Markus Leippold for his assistance throughout the project and for allowing me to deal with this topic. I am grateful to Roberto Frassanito, Federica Mazzucato, Nicolas Curin and the whole team at UBS-Market Risk Control for their availability, patience and for the help they provided.

Contents
1 FX Exotic Options - an overview 1.1 Introduction . . . . . . . . . . . . . . . . 1.2 Barrier options . . . . . . . . . . . . . . 1.2.1 Barrier Options Market . . . . . 1.2.2 Pricing Barrier Options . . . . . . 1.3 Digital Options . . . . . . . . . . . . . . 1.3.1 Payoff . . . . . . . . . . . . . . . 1.3.2 Pricing . . . . . . . . . . . . . . . 1.4 One-touch digital options . . . . . . . . . 1.4.1 Payoff . . . . . . . . . . . . . . . 1.4.2 Pricing one-touch digital options 1.5 Double Barrier Options . . . . . . . . . . 1.6 Other Exotic Options . . . . . . . . . . . 7 7 8 8 9 15 15 15 16 16 17 18 19 21 21 24 27 30 31 34 36

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2 Hedging FX Exotic Options 2.1 The Hedging Problem . . . . . . . . . . . . . . . . . . 2.2 Static Hedging: the Carr, Ellis and Gupta method . . . 2.3 Static Hedging: the Derman, Ergener and Kani method 2.4 Static Hedging: the Mean-Square method . . . . . . . 2.5 Static Hedging: alternative methods and model risk . . 2.6 Static hedging of digital options . . . . . . . . . . . . . 2.7 Static hedging of double barrier options . . . . . . . . .

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3 Risk managing a portfolio of FX options 38 3.1 Methodology . . . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.2 Risk control for portfolio of FX exotic options . . . . . . . . . 41 4 Conclusion 48

Chapter 1 FX Exotic Options - an overview
1.1 Introduction

FX markets are among the most liquid markets in the world, since the FX trading is nowadays global and almost continuous. FX options market is rapidly expanding, being the fastest growing segment of the FX market. Due to the liquidity of the underlying and the simple relationship between forward and spot prices, beside plain vanilla options a wide variety of exotic derivatives have been marketed. These exotic options have been produced by banks and other financial institutions to match corporate end-users and investors’ requirements: either to reduce premium expenditure, or to better fit the risk profile of the client. Exotic options are mainly traded in Over-The-Counter (OTC) markets and banks have a major role as market makers. As the trading in FX derivatives is developing fast, most of the institutions that offer services in FX options have now teams of mathematicians and physicists devoted to exotics. Their job is to find the right valuation, basic...
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