The Impact of Jumps in Volatility and Returns

TLDR

The paper investigates continuous‑time models that include jumps in returns and volatility alongside diffusive stochastic volatility. The authors estimate the models with a likelihood‑based approach, fitting parameters, spot volatility, jump times and sizes to S&P 500 and Nasdaq 100 returns, and compare model performance using implied volatility curves from option prices. The study finds that jumps in volatility and returns are significant, especially during market stress, and that estimation uncertainty in parameters and spot volatility differentially affects option pricing.

Abstract

This paper examines a class of continuous-time models that incorporate jumps in returns and volatility, in addition to diffusive stochastic volatility. We develop a likelihood-based estimation strategy and provide estimates of model parameters, spot volatility, jump times and jump sizes using both S&P 500 and Nasdaq 100 index returns. Estimates of jumps times, jump sizes and volatility are particularly useful for disentangling the dynamic effects of these factors during periods of market stress, such as those in 1987, 1997 and 1998. Using both formal and informal diagnostics, we find strong evidence for jumps in volatility, even after accounting for jumps in returns. We use implied volatility curves computed from option prices to judge the economic differences between the models. Finally, we evaluate the impact of estimation risk on option prices and find that the uncertainty in estimating the parameters and the spot volatility has important, though very different, effects on option prices.