FX Options and Smile Risk (PDF)

Preface. Notation and Acronyms. 1 The FX Market. 1.1 FX rates and spot contracts. 1.2 Outright and FX swap contracts. 1.3 FX option contracts. 1.4 Main traded FX option structures. 2 Pricing Models for FX Options. 2.1 Principles of option pricing theory. 2.2 The black-scholes model. 2.3 The Heston Model. 2.4 The SABR model. 2.5 The mixture approach. 2.6 Some considerations about the choice of model. 3 Dynamic Hedging and Volatility Trading. 3.1 Preliminary considerations. 3.2 A general framework. 3.3 Hedging with a constant implied volatility. 3.4 Hedging with an updating implied volatility. 3.5 Hedging Vega. 3.6 Hedging Delta, Vega, Vanna and Volga. 3.7 The volatility smile and its phenomenology. 3.8 Local exposures to the volatility smile. 3.9 Scenario hedging and its relationship with Vanna-Volga hedging. 4 The Volatility Surface. 4.1 General definitions. 4.2 Criteria for an efficient and convenient representation of the volatility surface. 4.3 Commonly adopted approaches to building a volatility surface. 4.4 Smile interpolation among strikes: the Vanna-Volga approach. 4.5 Some features of the Vanna-Volga approach. 4.6 An alternative characterization of the Vanna-Volga approach. 4.7 Smile interpolation among expiries: implied volatility term structure. 4.8 Admissible volatility surfaces. 4.9 Taking into account the market butterfly. 4.10 Building the volatility matrix in practice. 5 Plain Vanilla Options. 5.1 Pricing of plain vanilla options. 5.2 Market-making tools. 5.3 Bid/ask spreads for plain vanilla options. 5.4 Cutoff times and spreads. 5.5 Digital options. 5.6 American plain vanilla options. 6 Barrier Options. 6.1 A taxonomy of barrier options. 6.2 Some relationships of barrier option prices. 6.3 Pricing for barrier options in a BS economy. 6.4 Pricing formulae for barrier options. 6.5 One-touch (rebate) and no-touch options. 6.6 Double-barrier options. 6.7 Double-no-touch and double-touch options. 6.8 Probability of hitting a barrier. 6.9 Greek

Antonio Castagna is currently partner and co-founder of the
consulting company Iason ltd, providing support to financial
institutions for the design of models to price complex derivatives
and to measure a wide range of risks, including credit and
liquidity. Antonio graduated in Finance from LUISS University,
Rome, in 1995 with a thesis on American options and the numerical
procedures for their valuation. He began his career in investment
banking in IMI Bank, Luxemborug, as a financial analyst in the Risk
Control Department before moving to Banca IMI, Milan, first as a
market maker of cap/floors and swaptions, before setting up the FX
options desk and running the book of plain vanilla and exotic
options on the major currencies, whilst also being responsible for
the entire FX volatility trading.

Antonio has written a number of papers on credit derivatives,
managing of exotic options risks and volatility smiles. He is often
invited to academic and post-graduate courses.

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