Estimación bayesiana del modelo de difusión con saltos de Merton

Abstract

On the Bayesian Estimation of Merton's Jump Diffusion Model 

In the literature there are different contributions on how to identify the evolution of financial derivatives via underlying asset prices. The Jump-difussion-Merton’s model (JDMM) is one of the most important references to model the stochastic dynamics of asset returns in comparison with the Black and Scholes (B&S) model. The main objective of this paper is to perform a comparative analysis between the JDMM and the B&S from a Bayesian approach using Markov-Chain-Monte-Carlo (MCMC) methods.

Simulations applied to the daily log of some of the main stocks that make up the NASDAQ index evidenced the superiority in goodness of fit of the JDMM over financial returns via MCMC. Some recommendations and limitations of this research arise in the appropriate proposal for the values used as parameters for the prior distributions used before estimating the posterior distributions for each parameter of each model.

The major contribution within the statistical framework of this research is illustrating the effectiveness of the MCMC methods for the JDMM in juxtaposition to B&S.