Option-Implied Intrahorizon Value at Risk

Abstract

In this paper, we theoretically and empirically study the intrahorizon value at risk (iVaR) in a general jump-diffusion setting. We propose a new class of models of asset returns, the displaced mixed exponential model, which can arbitrarily closely approximate finite and infinite activity Lévy processes. We then derive analytical results for the iVaR and disentangle, in a theoretically consistent way, the jump and diffusion contributions to the intrahorizon risk. We estimate historical and option-implied value at risk and iVaR for several popular jump models using the Standard & Poor’s (S&P) 100 Index and American options. Empirically disentangling the contribution of the jumps from the contribution of the diffusion, we conclude that jumps account for about 90% of the iVaR on average. Our back-testing results indicate that the option-implied estimates are much more responsive to market changes than their historical counterparts, which perform poorly. This paper was accepted by Gustavo Manso, finance.