Multi-currency FX derivatives o?er 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 ?nancial 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 a?ne 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.
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.
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