Estimating the basis risk of index-linked hedging strategies using multivariate extreme value theory

Abstract

This paper studies the empirical quantification of basis risk in the context of index-linked hedging strategies. Basis risk refers to the risk of non-payment of the index-linked instrument, given that the hedger’s loss exceeds some critical level. The quantification of such risk measures from empirical data can be done in various ways and requires special consideration of the dependence structure between the index and the company’s losses as well as the estimation of the tails of a distribution. In this context, previous literature shows that extreme value theory can be superior to traditional methods with respect to estimating quantile risk measures such as the value at risk. Thus, the aim of this paper is to conduct an empirical analysis of basis risk using multivariate extreme value theory and extreme value copulas to estimate the underlying risk processes and their dependence structure in order to obtain a more adequate picture of basis risk associated with index-linked hedging strategies. Our results emphasize that the application of extreme value theory leads to better fits of the tails of the marginal distributions in the considered stock price sample and that traditional methods in regard to estimating marginal distributions tend to overestimate basis risk, while basis risk can in contrast be higher when taking into account extreme value copulas.