Title: On lead-lag correlations in stochastic volatility models with jump
Authors: Sujay Mukhoti - Indian Institute of Management Indore (India) [presenting]
Pritam Ranjan - Indian Institute of Management Indore (India)
Abstract: In an efficient market, the returns and their time dependent volatility are often jointly modelled by stochastic volatility models (SVMs). SVM posits the current return as a function of current latent volatility in a hierarchical model. Volatility is further modelled as an auto-regressive process. In an attempt to include the opposite reaction of return to its volatility, the return and volatility shocks are assumed to be negatively correlated (SVL-I), which however leads to violation of the efficient market hypothesis. Subsequently, a host of alternative SVMs (SVL-II) had been developed where current return shock is assumed to be correlated with future volatility shock. On the contrary, recent empirical works provides support for a strong contemporaneous correlation between return and volatility. The SVL-II models, however, fails to account for such contemporaneous correlation. We propose a correction of the SVL-I type models to satisfy EMH and capture the contemporaneous correlation as well. We also establish theoretical results in support of empirical lead-lag correlation pattern between return and volatility. We inspect similar results in case of SVM with leverage and jumps. Furthermore, two real-life examples (Euro-USD rate, and S&P 500 index returns) have been used to demonstrate the performance of this new class of SVMs.