Mathematical Finance: A Verrazano Course Enrichment Project

Michael Siozios, Verrazano Class of 2015, did a special Verrazano course enrichment project in an upper-level mathematics course during the fall semester.  Read below to hear from Michael about what he learned from the course and the project.

Michael Siozios, Class of 2015

Hello, my name is Michael Siozios, and my majors are Mathematics and Finance. I am part of the Verrazano Class of 2015.

My Fall 2014 semester was awesome to say the least. I had a research experience unlike any other, in which I was lucky to witness, in action, all of the mathematics I’ve had exposure to my entire life. Thank you to the Verrazano Program for making this possible. I interacted directly with mathematical finance, utilizing the mechanics necessary for future study in financial engineering. My course material and the research project made me aware that the depth of knowledge necessary to be fluent in this field is vast.

I was able to see and understand a beautiful derivation of the Black and Scholes formula used to price options available for sale in the financial markets. The techniques used to price options are amazing. My favorite part of pricing options is that the methods financial engineers and banks apply hedge an option that writers position to be risk neutral in theory.  Hedging, in investment terms, means that investors use strategies and instruments to try to reduce or offset risk as much as possible. I see why the options market has grown over time to be a tremendous industry.

The course strategy was amazing and taught with passion, giving the class a great perspective on the material. We obtained a thorough understanding of the discrete elements of the course, and by employing methods learned in continuous probability, we were able to move into the continuous, and thus more realistic, world nicely.

Programming was a focus of my research outside of the classroom, and I analyzed and compared models designed to price options appropriately.  A “correct” option price eliminates arbitrage opportunities.  Arbitrage is when someone buys in one market and, at the same time, sells in another market without much, if any, financial risk. I learned that after many instances of time accounted for discretely using the binomial option pricing model, one may price options nicely. Otherwise, one may use the Black Scholes formula. Why am I interested in this material? It’s simple: options have been a key component in finance for a long time, and they allow individuals to hedge their investments. It has even given rise to other practices like option trading. These are business opportunities available to everyone, making it possible for individuals to have a diversified portfolio and a varied source of income.

An important lesson learned in my research experience is that there is no upper limit to the knowledge of programming I should obtain. Many individuals prefer some languages over others; however, knowing multiple programming languages can be extremely beneficial to someone in the field of financial engineering.

All in all, although the demands of my courses and research combined were extensive, this experience was excellent. I have far more knowledge than previously, and I’ve acquired information necessary for my future career.