An Investigation of Model Risk in a Market with Jumps and Stochastic Volatility

Abstract

The aim of this paper is to investigate model risk aspects of variance swaps and forward start options in a realistic market setup where the underlying asset price process exhibits stochastic volatility and jumps. We devise a general framework in order to provide evidence of the model uncertainty attached to variance swaps even when the popular replication result is accounted for. Then, we consider the model risk of forward-start options and we show how this risk can be reduced by adding variance swaps in the set of calibration instruments. In the adopted framework, variance swaps and forward-start options can be valued by means of analytic methods. We measure model risk using a set of 21 models representing various dynamics with both continuous and discontinuous sample paths. To conduct our empirical analysis, we work with two major equity indices (S&P 500 and Eurostoxx 50) under different market situations.

Keywords: Risk Management, Model Risk, Robustness and Sensitivity Analysis, Variance Swap, Forward-start option

JEL Classification: D81, C52, G13