Abstract/Summary

Measuring model risk is required by regulators on financial and insurance markets. We first investigate the model risk for liquid products. We separate model risk into parameter estimation risk and model specification risk, and we propose expected shortfall type model risk measures applied to L´evy jump models and affine jump-diffusion models. We investigate the impact of parameter estimation risk and model specification risk on the models’ ability to capture the joint dynamics of stock and option prices. We estimate the parameters using Markov chain Monte Carlo techniques, under the risk-neutral probability measure and the real-world probability measure jointly. We find strong evidence supporting modeling of price jumps. We then turn our focus to model risk for illiquid products. We propose a methodology to measure the parameter estimation risk and model specification risk of pricing models, as well as model selection risk of model classes, based on realized payoffs, for products in the over-the-counter market. L´evy jump models and affine jump-diffusion models are applied in estimating the fair variance strikes of variance swaps and forward starting option prices. Our results show that both parameter estimation risk and model specification risk are significant for variance swaps, while model specification risk is dominant when pricing forward starting options. We also find that the size of the model selection risk is substantial for both products. We further study the forward-looking market risk premium (FMRP) and its economic implications. The FMRP is a function of investors’ risk aversion and forward-looking volatility, skewness, and kurtosis of cumulative returns. Using the S&P 500 index returns and VIX, we estimate the monthly FMRP from 1999 to 2020. We find that the FMRP estimated from the stochastic volatility model with a mean-reversion variance process adequately reflects market conditions and is always positive. We also find that the FMRP is significantly positively linked to the future market sentiment and is significantly negatively linked to the future growth of real economic activity proxies. Moreover, the market excess returns increase with FMRP in a bull market and decrease with FMRP in a bear market, implying that investors can only receive compensation for tolerating extra risk when the market is bullish.