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CCF Seminar
Mackenzie Wildman
Lehigh University
Title: A Gaussian Markov alternative to fractional Brownian motion for pricing financial derivatives

Abstract: I will introduce and discuss the Dobri\'{c}-Ojeda process, a Gaussian Markov It\^{o} diffusion process that approximates some characteristics of fractional Brownian motion. We replace Brownian motion in the Black-Scholes SDE with the Dobri\'{c}-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 Dobri\'{c}-Ojeda type noise in the stochastic heat equation and similarity in properties to fractional noise. This is joint work with Daniel Conus and Vladimir Dobri\'{c}.

Date: Monday, October 26, 2015
Time: 4:30 pm
Location: Wean Hall 8220
Submitted by:  Kasper Larsen