Multivariate Tests of a Continuous Time Equilibrium Arbitrage Pricing Theory with Conditional Heteroskedasticity and Jumps

This paper uses ML and GMM techniques to estimate systems of stochastic differential equations that describe the behaviour of stock returns. We test restrictions implied by a continuous time asset pricing model that builds on the work of Chamberlain (1988). The stochastic differential equations we estimate allow for mean-reverting stochastic volatility and for jumps of random size, and are therefore consistent with the observation that stock returns exhibit conditional heteroskedasticity and high unconditional kurtosis. We are able to distinguish whether excess kurtosis in returns simply reflects stochastic volatility or whether a satisfactory model requires in addition the inclusion of jump components. We examine whether the joint distribution of stock prices has changed between the two periods 1984 86, and 1987 89, and find that while the persistence in variance seemed to become somewhat less important, jumps in stock prices became more important.