The Quanto Adjustment and the Smile

摘要

European quanto derivatives are usually priced using the well-known quanto adjustment corresponding to the forward of the quantoed asset under the assumptions of the Black-Scholes model. In this article, I present the quanto adjustment corresponding to the local volatility model that allows pricing quanto derivatives consistently with the observed market equity skew and exchange rate smile. I then examine the model risk arising in the standard quanto adjustment by fitting the local volatility model to market data and then comparing the prices of European quanto euro derivatives on the Nikkei 225 index with those generated by the standard quanto adjustment. The results show that the standard quanto adjustment can be subject to significant pricing errors when compared with the local volatility model. I also compare the pricing performance of the local volatility model with a multivariate stochastic volatility model. The results show that when the correlation between the instantaneous variances associated with the underlying asset and the exchange rate is close to one, as it is the case when we consider historical data, there is little evidence of model risk for the local volatility model in the pricing of European quanto euro derivatives on the Nikkei 225 index.