In this article we focus on how to combine important sampling techniques within Markov chain Monte Carlo methods, particularly the Gibbs sampler. We propose a way for constructing a change of measure with respect to the intractable target joint distribution of the sampler by\ employing proper...

To implement continuous time option pricing models in which ARCH models can be used as direct or indirect approximators of stochastic volatility, we construct continuous time economies exhibiting equilibrium dynamics to which most asymmetric ARCH models converge in distribution as the sample...

We compare the state-price density that is implied by the cross-section of options prices with the corresponding density of the underlying asset price that is derived from an equilibrium model with Markovian stochastic volatility. If the data-generating process is of the stochastic volatility...