Smile Risk in Expected Shortfall Estimation for Interest Rate Options

Abstract

This thesis aims to further develop historical simulation methods and focuses on the market risk of interest rate options in the presence of negative interest rates. To accommodate these negative interest rates, a typical solution is to shift the interest rates to lift them into positive territory, where the conventional pricing functions can be used again. We derive an adaptation of the SABR formula that allows us to compare implied volatilities obtained with different shift parameters. Using this method we are able to find risk factors that can be used to perform a historical simulation without the need for numerical calibration algorithms. Furthermore, we investigate if the currently applied methods can be improved by incorporating additional risk factors that can account for changes in the shape of the volatility smile.

Our results show that the studied historical simulation methods can provide accurate prediction of both the value at risk and the expected shortfall. However, we do not find strong evidence to support that modeling volatility smile changes improves the accuracy of a historical simulation.