Dan Scansaroli's Ph.D. defense 12-1-11

DISSERTATION DEFENSE ANNOUNCEMENT

TITLE:                    Stochastic Modeling with Temporally Dependent Gaussian Processes: Applications to Financial Engineering, Pricing and Risk Management

SPEAKER:            Daniel J. Scansaroli, PhD Candidate Department of Industrial and Systems Engineering

DATE:                   Thursday, December 1, 2011 from 3:00 – 5:00 pm

LOCATION:         Room 375, Mohler Laboratory, 200 W. Packer Avenue

ABSTRACT: This thesis studies two classes of the most often applied temporally dependent Gaussian processes. Computationally efficient and accurate techniques are
developed for modeling and parameter estimation with the goal of improving decision making, risk management, pricing and hedging in finance.

We first focus on the widely used fractional Brownian motion (fBm) processes. We explore the advantages and disadvantages of modeling with the processes and present
new consistent estimators of the Hurst index for a Weiner type fBm process. Simulation studies demonstrate that the new estimators are highly competitive to leading estimators
in accuracy, especially on small data sets, and much more time efficient. This makes the estimators ideal for fast paced financial markets, which is demonstrated on a variety of indices.
We conclude our study by demonstrating that the dependency structure of fBm may explain the term structure of volatility commonly observed in practice.

The second part of this presentation focuses on Gaussian Markov (GM) processes. GM processes allow for a wide range of properties including long or short-range dependence,
 non-stationarity, and heteroscedasticity. We prove that the quadratic variation leads to a new, computationally efficient, consistent estimator of a model’s diffusion parameter.
Consistency is proven on a finite time interval, making it well suited for real world applications. This contrasts with existing MLE methods that require an infinite time horizon for
consistency. The convergence rate and confidence interval bounds for the estimator are also obtained. We demonstrate how the quadratic variation changes Option Pricing Theory
and extend the Black-Scholes formula for general continuous sample path GM processes.

The accuracy of diffusion parameter estimation techniques is demonstrated by simulating an Ornstein-Uhlenbeck process and applying the quadratic variation and Maximum Likelihood
estimators. We use the Likelihood function to express all model parameter estimators in closed-form, eliminating the need for estimation through three dimensional numerical optimization methods.

The final part of the presentation addresses the pricing of American style derivatives through the discretization of any continuous path GM processes into a recombining n-period binomial tree. The
Central Limit Theorem for Stochastic Processes is used to prove that the tree converges to its continuous path GM process. We apply our method to create a tree for the Vasicek interest rate model
and price an American put option.

BIOGRAPHY: Daniel Jonathan Scansaroli is a Ph.D. candidate in the Department of Industrial and Systems Engineering at Lehigh University. Educated at Lehigh for both undergraduate and graduate
degrees, he received a Bachelor of Science in Mechanical Engineering in 2005. Awarded Lehigh University's Presidential Scholarship, he received the degree of Master of Science in
Applied Mathematics in May 2006 and a Master of Science in Management Science in January 2009. Currently, Dan is employed in asset management as a quantitative analyst for
Lehigh University's endowment office.