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This paper presents a general framework for pricing multi-asset cross currency options under a broad class of multi-dimensional diffusion models. We notice that the underlying assets of a multi-asset cross currency option are related with multiple underlying asset markets as well as at least one currency market. Moreover, it is necessary for practical use of a pricing model to take the information of each underlying asset’s option market into account. Then, calibration to each option market needs a more complex model than Black-Scholes model such as stochastic volatility models to reflect the skew/smile and term structure of implied volatilities observed in the option market. Thus, a multidimensional diffusion model should be applied to pricing a multi-asset cross currency option and relevant calibrations, where an analytical valuation method is necessary
for fast computation. On the other hand, it is almost impossible to obtain a closedform option pricing formula under a multi-dimensional diffusion setting. An effective method for overcoming this problem is an asymptotic expansion scheme which is a uni-fied method in order to achieve accurate approximations of option prices and Greeks in multi-dimensional models. (For instance, please see [36], [27], [28], [20], [31], [32], [29],[30] for the detail.) We also remark that the Mathematical foundation of this method … to download http://www.carf.e.u-tokyo.ac.jp/pdf/workingpaper/fseries/288.pdf

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