Speaker: Mackenzie Wildman, Lehigh University
Slides: ( TBA )
ABSTRACT
I will introduce and discuss the Dobric-Ojeda process, a Gaussian Markov Ito diffusion process that approximates some characteristics of fractional Brownian motion. We replace Brownian motion in the Black-Scholes SDE with the Dobric-Ojeda process to incorporate temporal dependence of stock prices. I will discuss recent work towards describing a risk-neutral measure under this stock price process. Additionally, I will discuss some parameter estimation techniques and implementation of this model and comparison with historical option prices. Time permitting, I will also discuss recent work in applying a Dobric-Ojeda type noise in the stochastic heat equation and similarity in properties to fractional noise. This is joint work with Daniel Conus and Vladimir Dobric.