When: 
Wednesday, May 3, 2017 - 12:15pm - 1:00pm
Where: 
Pardee 217
Presenter: 
Ha My Bui '17
Price: 
Free & there will be pizza!

This paper presents several different stochastic volatility models for option-pricing popular in literature, focusing on Bates, Double-jump, and Variance Gamma model. With evidence of the volatility smile, the constant volatility parameter in Black-Scholes model proves to be insufficient to provide a good fit of model estimations with real data. Mixed-jump diffusion models such as these allows return in stock price to not only move in small increments determined by a normal distribution, but also experience big, crash-like movements such as in a crisis. In all three models, volatility is a stochastic process, capturing more effectively the behavior of stock price in the real world.

 Simulation shows that these models generate stock price paths with distribution close to log-normal, with the Variance Gamma model generating more outliers of stock price far away from starting price. In order to estimate parameters in these models, we used Bayesian inference techniques to obtain their distributions and provided detailed derivation steps to derive the posterior distributions. We also made adjustments to the models used to ensure stock price grows at the desired growth rate. In addition, Markov Chain Monte Carlo simulation is utilized to update the parameters. The results have fairly large standard errors and are fairly sensitive to the choice of initial settings.

 

Sponsored by: 
Department of Mathematics

Contact information

Name: 
C. Jayne Trent
Phone: 
610-330-5267
Email: 
trentj@lafayette.edu