Robustness of the Multivariate Black-Scholes Model

This thesis provides an extension to the tracking error derived in El Karoui, Jeanblanc-Picquè and Shreve (1998). We establish a hedging error in a multivariate setting, where assets have a misspecified correlation. For this, we consider the case where the misspecified correlations are at most stochastic in the sense that they depend on the current prices of the underlyings, where the trader makes use of classical delta-hedging, while we allow for true correlations to be stochastic. We illustrate the theoretical results by a numerical study on two-asset options, where we first assume that the true and the misspecified correlations are constant and then consider the case where the true correlation is in fact stochastic. Furthermore, we derive the tracking error in the two-dimensional case where both the true and the misspecified correlation are stochastic and where the trader must invest into a derivative in order to hedge the correlation risk.