Multi-currency FX derivatives offer a challenging playground to the mathematical modelling of correlations. Quotes of liquidly traded vanilla options on cross FX rates, e.g. EUR/JPY, can be used to extract a great deal of information about the complex implied correlation structure between the corresponding main FX rates, e.g. USD/JPY and EUR/USD. Including all this information in a financial model means being able to fit simultaneously all volatility smiles, a very demanding task. In this paper we propose a first solution to this problem in the class of stochastic volatility models. We introduce a novel multi-factor stochastic volatility Heston-based model, which is able to reproduce consistently typical multi-dimensional FX vanilla markets, while retaining the (semi)-analytical tractability typical of affine models and relying on a reasonable number of parameters. A successful joint calibration to real market data is presented together with various in- and out-of-sample calibration exercises to highlight the robustness of the parameters estimation. The proposed model is symmetric with respect to the choice of the risk-free currency , opening up to new approaches for coherent pricing and risk management of derivatives depending on multiple currencies .
 We introduce a novel multi-factor Heston-based stochastic volatility model, which is able to reproduce consistently typical multi-dimensional FX vanilla markets, while retaining the (semi)-analytical tractability typical of affine models and relying on a reasonable number of parameters. A successful joint calibration to real market data is presented together with various in- and out-of-sample calibration exercises to highlight the robustness of the parameters estimation. The proposed model preserves the natural inversion and triangulation symmetries of FX spot rates and its functional form, irrespective of choice of the risk-free currency . That is, all currencies are treated in the same way .
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Multi-currency FX derivatives offer a challenging playground to the mathematical modelling of correlations. Quotes of liquidly traded vanilla options on cross FX rates, e.g. EUR/JPY, can be used to extract a great deal of information about the complex implied correlation structure between the corresponding main FX rates, e.g. USD/JPY and EUR/USD. Including all this information in a financial model means being able to fit simultaneously all volatility smiles, a very demanding task. In this paper we propose a first solution to this problem in the class of stochastic volatility models.
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stochastic volatility Heston-based
Heston-based stochastic volatility
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is symmetric with respect to the
preserves the natural inversion and triangulation symmetries of FX spot rates and its functional form, irrespective of
R
, opening up to new approaches for coherent pricing and risk management of derivatives depending on multiple currencies
. That is, all currencies are treated in the same way