Time-Varying Uncertainty and Jump Intensities: Why Should Variance Jumps Be Different?
59 Pages Posted: 9 May 2017
Date Written: April 3, 2017
A major assumption of many financial models is that return jump intensities are proportional in the stochastic uncertainty of the underlying. Transferring this intuition to volatility jumps requires that in affine models the variance jump intensity is associated with changes in the stochastic variance-of-variance (q), not with changes in the local variance (V). A model-free analysis shows that the local variance-of-variance describes risk-neutral variance jump expectations well across different maturities, whereas the local variance has almost no explanatory power. The analysis suggests further that q relates to short-term jump expectations on stock return level. The two competing hypotheses of V- and q-associated variance jumps are included separately and jointly in VIX option pricing models. The results show that a single upward variance jump specification with an intensity that is affine in q leads to the best pricing results. This alternative modeling of the jump intensity has two implications for the variance dynamics. First, the local variance is estimated to be much higher in times of crises, whereas its long-run stochastic mean remains at lower levels. Second, the vol-of-vol risk-premium increases to 6-7%, which is else close to zero.
Keywords: Variance Jumps, Volatility-of-Volatility, VIX
JEL Classification: G13
Suggested Citation: Suggested Citation