Senior Project, University of Maryland

To fulfill the requirements for Departmental Honors in Mathematics at the University of Maryland, I worked for 4 semesters with Brian Hunt, a member of the Chaos Group.

We studied chaotic orbits of the quadratic map, at parameter values near transitions to periodicity. We studied the autocorrelations of these orbits, because we wished to find some characteristic of the orbits that would reflect the imminent onset of periodicity.

We found that the autocorrelation scaled very regularly with the distance from the periodic regime. The scaling behavior was well represented by a power law, and we found that the exponent in the power law was dependent on the size of the window.

TeX source, Cover Page, Body of the paper, Figures

Master's Thesis, NYU/MIT

To finish my Master's Thesis through NYU, I worked with Martin Bazant at MIT. We studied techniques of random walks and diffusions in generalizing the Black-Scholes model of option pricing.

Writeup: Postscript, TeX source.

In addition, I continued this work a little after finishing the degree requirements. Some stuff associated with this work:

My full research log: Postscript, TeX source
Matlab sub for computing the unit normal cdf: N.m
Matlab sub for computing Hermite polynomials 0-6: hermite.m
Matlab routines for pricing caplets and floorlets by Black's model, and for solving for the implied volatility: Black_price.tgz
Matlab routines for pricing European calls and puts by the Black-Scholes model, and for solving for the implied volatility: BlackScholes_price.tgz
Matlab routine for pricing European calls, using the more generalized pricing methodology of the research write-up: Bouchaud_price.tgz

The research log refers several times to the Lecture and Appendix written by Prof. Bazant. I have placed these documents here: Lecture and Appendix. These documents are also available at Prof. Bazant's web site.