Dynamic jump intensities and risk premiums: Evidence from S&P500 returns and options

We build a new class of discrete-time models that are relatively easy to estimate using returns and/or options. The distribution of returns is driven by two factors: dynamic volatility and dynamic jump intensity. Each factor has its own risk premium. The models significantly outperform standard models without jumps when estimated on S&P500 returns. We find very strong support for time-varying jump intensities. Compared to the risk premium on dynamic volatility, the risk premium on the dynamic jump intensity has a much larger impact on option prices. We confirm these findings using joint estimation on returns and large option samples.     

Lévy jump risk: Evidence from options and returns

Using index options and returns from 1996 to 2009, I estimate discrete-time models where asset returns follow a Brownian increment and a Lévy jump. Time variations in these models are generated with an affine GARCH, which facilitates the empirical implementation. I find that the risk premium implied by infinite-activity jumps contributes to more than half of the total equity premium and dominates that of the Brownian increments suggesting that it is more representative of the risks present in the economy. Overall, my findings suggest that infinite-activity jumps, instead of the Brownian increments, should be the default modeling choice in asset pricing models.     

Option valuation with long-run and short-run volatility components

This paper presents a new model for the valuation of European options, in which the volatility of returns consists of two components. One is a long-run component and can be modeled as fully persistent. The other is short-run and has a zero mean. Our model can be viewed as an affine version of Engle and Lee [1999. A permanent and transitory component model of stock return volatility. In: Engle, R., White, H. (Eds.), Cointegration, Causality, and Forecasting: A Festschrift in Honor of Clive W.J. Granger. Oxford University Press, New York, pp. 475–497], allowing for easy valuation of European options. The model substantially outperforms a benchmark single-component volatility model that is well established in the literature, and it fits options better than a model that combines conditional heteroskedasticity and Poisson–normal jumps. The component model's superior performance is partly due to its improved ability to model the smirk and the path of spot volatility, but its most distinctive feature is its ability to model the volatility term structure. This feature enables the component model to jointly model long-maturity and short-maturity options.