Option pricing under time-varying risk aversion with applications to risk forecasting

Abstract

In this dissertation we present a new option pricing model - called the 2-Factor SV (stochastic volatility) model - which allows to account for time-varying risk aversion. Thereby, we are able to capture the empirical properties of pricing kernels, such as time-variation and the typical S-shape, which is important in order to extract the forward-looking information from option prices. Moreover, the 2-Factor SV model allows to discover the risk preferences of market participants through time. Within an empirical study we apply the 2-Factor SV model by analyzing the risk preferences of market participants from 2001 to 2009 based on S&P 500 index options. We find that risk aversion of market participants strongly increases during stressed market conditions and relaxes during normal market conditions. Moreover, we find that market participants are risk seeking some time before the subprime mortgage crises. In the second part of the empirical study we analyze the ability of the 2-Factor SV model to extract the forward-looking information from option prices. We therefore perform Value-at-Risk (VaR) forecast for the S&P 500 index during the period of the subprime mortgage crises. In order to better classify the corresponding forecasting results, we also perform VaR forecasts based on three alternative VaR models, namely the Black-Scholes and the Heston model, which also rely on option-implied information, and the GARCH model, which relies on historical return information. As a result, the 2-Factor SV model has the best forecasting performance, followed by the Black-Scholes, the Heston and the GARCH model. In particular, the 2-Factor SV model is the only one, which is able to perform highly accurate VaR forecasts for all confidence levels (95 %, 99 % and 99.9 %) and forecasting horizons (1, 2, 3 and 4 weeks) despite the challenging forecasting period.