Stochastic Volatility Model with Jumps in Returns and Volatility: Performance and Implementation

This thesis examines the performance and implementation of the stochastic volatility model with jumps in return and volatility (SVCJ) of Duffle et al. (2000), and compares it to a GARCH(1,1) to assess whether SVCJ is worth the effort needed for its usage; we then propose directives to ease its implementation. Using Markov Chain Monte Carlo as the estimation method, and an algorithm written in R language, we estimate the SVCJ model on FTSE 100 daily returns from July 3, 1984 to December 29, 2006. Our algorithm produces parameter estimates and state variable paths. The program is also able to perform convergence and performance analysis on the output using trace plots, ACF plots and analyzing the error terms. Our results confirm that SVCJ model is able to identify not only jumps related to worldwide periods of market stress such as the 1987 and 2002 market crashes, but also those specific to domestic crises such as the UK crisis of September 1992. Moreover, our estimated unconditional mean of returns jump size is negative, implying that jumps in returns are due to bad news most of the time or that bad news have a bigger effect on returns than good news, causing relatively larger jumps in absolute value. Furthermore, our results show that SVCJ model outperforms GARCH, and the difference between the two models increases significantly with the presence of jumps.