Bayesian Analysis Of Asymmetric Double Exponential Jump-Diffusion Model

The asymmetric double exponential jump-diffusion model proposed by Kou(2002) is a simple jump-diffusion model. The model can provide explanation for asymmetric leptokurtic features and volatility smile, also it can produce analytical solutions for a variety of option-pricing problems. However, Kou did not estimate the asymmetric double exponential jump-diffusion model when the model was put forward, thus the paper uses Markov chain Monte Carlo (MCMC) method to estimate the model.First this paper surveys and assesses the development and main fruit of continuous-time equity return models since the BS model came on the scene, and estimation methods of these models are discussed. Then MCMC method is mainly studied in this paper, and how to use MCMC method to estimate continuous-time equity return models is introduced.At last, the MCMC method is used to estimate parameters of the asymmetric double exponential jump-diffusion model. The approach is based on Euler scheme, and it uses the likelihood of the discredited process as the approximate posterior likelihood. Then the paper uses C++ to complete MCMC method based MH algorithm which is applied to a wide class of models including systems with unobservable state variables, and estimates the parameters of the model. Through the study, we demonstrate that the MCMC method provides a useful tool in analysing the models including systems with unobservable state variables such as asymmetric double exponential jump-diffusion model, at the same time it is shown that the asymmetric double exponential jump-diffusion model exhibits many of the stylized facts about asset returns documented in the discrete-time financial econometrics literature, such as higher peak and thick tails.