Gibbs sampler with jump diffusion model: application in European call option and annuity

TL;DR

This paper introduces a Gibbs sampler-based method for estimating market parameters in jump diffusion models and demonstrates its application in pricing European call options and annuities, highlighting jump effects.

Contribution

It presents a novel Gibbs sampling approach for estimating jump diffusion market parameters and applies it to option and annuity pricing under jump risk.

Findings

Effective estimation of jump diffusion parameters

Impact of jump effects on option prices

Comparison with conventional models

Abstract

In this paper, we are presenting a method for estimation of market parameters modeled by jump diffusion process. The method proposed is based on Gibbs sampler, while the market parameters are the drift, the volatility, the jump intensity and its rate of occurrence. Demonstration on how to use these parameters to estimate the fair price of European call option and annuity will be shown, for the situation where the market is modeled by jump diffusion process with different intensity and occurrence. The results is compared to conventional options to observe the impact of jump effects.