Option Pricing Under Time-Varying Risk-Aversion with Applications to Risk Forecasting

Abstract

We present a new option-pricing model, which explicitly captures the difference in the persistence of volatility under historical and risk-neutral probabilities. The model also allows to capture the empirical properties of pricing kernels, such as time-variation and the typical S-shape. We apply our model for two purposes. First, we analyze the risk preferences of market participants invested in S&P 500 index options during 2001-2009. We find that risk-aversion strongly increases during stressed market conditions and relaxes during normal market conditions. Second, we extract forward-looking information from S&P 500 index options and perform out-of-sample Value-at-Risk (VaR) forecasts during the period of the subprime mortgage crises. We compare the VaR forecasting performance of our model with four alternative VaR models and find that 2-Factor Stochastic Volatility models have the best forecasting performance.

Keywords: Pricing kernel, Option pricing, Implied risk premium, Value-at-Risk forecast

JEL Classification: G12, G13, G14