The Quantitative Finance Library

Quantos and FX Skews We study the impact of the FX skew on quanto convexity adjustments. Using a double shifted lognormal model allows an easy calibration to the skews as well as expressing the FX skew impact analytically for quanto forwards. We conclude that under non stressed market conditions (σ^2 T≪1) the impact is negligible for short maturities and still not material for longer maturities compared to correlation risk. However, under stressed market conditions or if quanto products become liquid enough to provide market implied correlation, we would switch from a mark-to-model with uncertain correlation to a mark-to-market with implied correlation. In this situation we will need to incorporate the FX skew. In a second study, we emphasis the drawbacks of modelling FX with shifted-lognormals and as an alternative we introduce the double mixture of lognormals model as the easiest model compatible with the flat lognormal quanto adjustment formula. , J.Pantz (2011)

A Class of Levy Process Models with almost exact calibration of both barrier and vanilla FX options Vanilla (standard European) options are actively traded on many underlying asset classes, such as equities, commodities and foreign exchange. The market quotes for these options are typically used by exotic options traders to calibrate the parameters of the (risk-neutral) stochastic process for the underlying asset. Barrier options, of many different types, are also widely traded in all these markets but one important of the FX Options market is that barrier options, especially Double-no-touch (DNT) options, are now so activley traded that they are o longer considered, in ay way, exotic options. Instead, traders would, in principle, like ot use them as instruments to which they can calibrate their model. The desirability of doing this has been highlighted by talks at practitioner conferences but, to our best knowledge (at least within the realm of the published literature), there have been no models which are specifically designed to cater for this. In this paper, we indtoruce such a model. It allows for calibration in a two-stage process. The first stage fits to DNT options (or other types of double barrier options). The seocnd stage fits to vanilla options. The model allows for jumps (ether finite activity or infinite activity) and also for stochastic volatility. Hence, not only can it give a good fit to the market prices of options, it can also allow for realistic dynamics of the underlying FX rate and realistic future volatility smiles and skews. En route, we significantly extend existing results in the literature by providing closed form (up to Laplace inversion) expressions for the prices of several types of barrier options as well as results related to the distribution of first passage times and of the ``overshoot'. , P.Carr, J.Crosby (2009)

FX Volatility Smile Construction The foreign exchange options market is one of the largest and most liquid OTC derivative markets in the world. Surprisingly, very little is known in the aca- demic literature about the construction of the most important object in this market: The implied volatility smile. The smile construction procedure and the volatility quoting mechanisms are FX specific and differ significantly from other markets. We give a detailed overview of these quoting mechanisms and introduce the resulting smile construction problem. Furthermore, we provide a new formula which can be used for an efficient and robust FX smile construction. , U.Wystup, D.Reiswich (2009)

Quanto Skew We assess the effect of an implied volatility skew for an FX rate on quanto forwards and quanto options of an asset that itself is sub ject to an implied volatility skew using a simplistic double displaced diffusion models. , P.Jaeckel (2009)

An arbitrage-free method for smile extrapolation We introduce a method for extrapolating smiles beyond an "observable" region that is consistent with no arbitrage. The extrapolation is not unique, but can be tuned e.g., to different power-law decays. This method has important applications in various areas such as the calculation of CMS rates, inverse FX options etc. , S.Benaim, M.Dodgson, D. Kainth (2009)

On the Valuation of Fader and Discrete Barrier Options in Heston s Stochastic Volatility Model , U.Wystup, S.Griebsch (2008)

Pricing Formulae for Foreign Exchange Options , U.Wystup (2008)

Vanna-Volga Pricing , U.Wystup (2008)

Modelling the FX Skew , D.Kainth, N.Saravanamuttu (2007)

Coupling Smiles , V.Durrleman, N.El Karoui (2007)

Pricing Multivariate Currency Options with Copula , M.Salmon, C.Schleicher (2006)

FX Basket Options , U.Haslet (2006)

Using Copulas to Construct Bivariate Foreign Exchange Distributions with an Application to the Sterling Exchange Rate Index , M.Hurd, M.Salmon, C.Schleicher (2006)

Consistent Pricing of FX Options , A. Castagna, F. Mercurio (2006)

Consistent pricing and hedging of an FX options book , L. Bisesti, A. Castagna, F. Mercurio (2005)

A Multi-currency Model with FX Volatility Skew , V. Piterbarg (2005)

A Stochastic Volatility Model for Risk-Reversals in Foreign Exchange , C.Albanese, A.Mijatovic (2005)

Stochastic Skew in Currency Options , P.Carr, L.Wu (2005)

FX Barriers with Smile Dynamics , G.baker, R.Beneder, A.Zilber (2004)

Pricing cross-currency forward options , A.Fordyce (2003)