Agenda

 Yacine Aït-Sahalia (Princeton University) - Testing Whether Volatility is Stochastic (joint work with Jean Jacod)

Abstract: There is broad empirical agreement that the volatility of most economic and financial state variables is time-varying. One way to capture this in continuous-time models is to make the volatility its own latent process, leading to a stochastic volatility model. Another, more restrictive, approach consists in making the volatility a function of the state variables themselves, leading to a local volatility model. This paper tests whether the generality afforded by stochastic volatility models is empirically necessary: can a semimartingale with stochastic volatility be simplified and written as one with local volatility instead? The proposed test is based on high frequency asymptotics, is robust to the presence of jumps and noise in the data, and requires only the computation of sums of increments of the observed state variables. The test is applied to stock price and interest data and suggests that stochastic volatility is a necessary feature of models for the former, while less so for the latter.