Bayesian Estimation of Asymmetric Jump-Diffusion Processes

Annals of Financial Economics BAYESIAN ESTIMATION OF ASYMMETRIC JUMP-DIFFUSION PROCESSES

The hypothesis that asset returns are normally distributed has been widely rejected. The literature has shown that empirical a<>set returns are highly skewed and Ieptokurtic. The affine jump-diffusion (AJD) model improves upon the normal specification by adding a jump component to the price process. Two important extensions proposed by Ramezani and Zeng (1998) and Kou (2002) further improve the...

Jump-Diffusion Processes on Matrix Lie Groups for Bayesian Inference

A variety of engineering problems can be studied as inferences on constrained sets, Lie groups in particular. Additionally, the number of parameters to be estimated, namely the model-order, may also be unknown a-priori. We present a Bayesian approach by building a posterior probability distribution on a countable unions of Lie groups and utilizing the jump-diffusion processes to generate optima...

Efficient estimation of default correlation for multivariate jump-diffusion processes

Evaluation of default correlation is an important task in credit risk analysis. In many practical situations, it concerns the joint defaults of several correlated firms, the task that is reducible to a first passage time (FPT) problem. This task represents a great challenge for jump-diffusion processes (JDP), where except for very basic cases, there are no analytical solutions for such problems...

Reversible jump MCMC for nonparametric drift estimation for diffusion processes

In the context of nonparametric Bayesian estimation aMarkov chainMonte Carlo algorithm is devised and implemented to sample from the posterior distribution of the drift function of a continuously or discretely observed one-dimensional diffusion. The drift is modeled by a scaled linear combination of basis functions with a Gaussian prior on the coefficients. The scaling parameter is equipped wit...

Asymmetric Jump Processes: Option Pricing Implications