Wednesday, February 11, 2015

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.

Exploring The City: 2014 VELA Highlights

One of the ways that Verrazano students learn outside of the classroom is by participating in Verrazano Extracurricular Learning Activities, or VELAs.  These are fun, interesting, and informative events that help students expand their knowledge, connect them with opportunities, prepare them for the future, and give them a well-rounded undergraduate experience.
Off-campus Double-VELAs are the highlight of the VELA calendar, and they allow students to get connected with the incredible resources and rich history of New York City.   In 2014, Verrazano students participated in a number of off-campus VELA excursions.   These included trips to the New York Public Library, Brooklyn Grange Rooftop Farm, the Steinway Piano Factory, the New York Transit Museum, the Museum of the City of New York, the Lower East Side Tenement Museum, and walking tours with Matt Postal - an architectural historian.  See some of the highlights below!

Steinway Piano Factory Tour  
Astoria, Queens


Brooklyn Grange Rooftop Farm
Brooklyn Navy Yard

Recent Developments of Lower Manhattan with Matt Postal, architectural historian

New York Transit Museum
Downtown Brooklyn

Museum of the City of New York
East Harlem

Joseph Inigo, Verrrazano Honors Class of 2013, has completed his first semester of a PhD program in Molecular Pharmacology and Cancer Therapeutics. He reflects on how earning a biochemistry degree and Verrazano honors at CSI, has prepared him for this next stage of his career.

Hello friends,

Just a month ago, I completed the first semester of my PhD program in Molecular Pharmacology and Cancer Therapeutics at the Roswell Park Cancer Institute. The winter break has given me time to reflect upon my experiences and I wish to share some of them with you. As I ready to type, with coffee in hand and a wintry view offered by the window beside me, my memory shifts to the previous spring. I was actually away for a conference where I was due to present my research on brain tumors, when I received an email from the Roswell Institute. They seemed pleased with my recent interview and more importantly, they had offered me acceptance into their graduate program. I welled up with great excitement and could not believe what I had just read. In fact, the next day I frequently looked for that same email just to make sure that it was not a dream I conjured the previous night.
Joseph Inigo on campus (during the day!)

Fast forward to the fall where I had just moved into my first apartment in downtown Buffalo. It was quite an adjustment that I had to make. Now in a new city filled with strangers, I felt as if I were starting my life from scratch. Although this stirred up a sense of apprehension, along with it came feelings of excitement and joy. I resolved to approach this new phase of my academic career with the utmost enthusiasm and vigor, in the same manner that one of my heroes, Theodore Roosevelt, would have (To my great surprise, the Theodore Roosevelt inaugural site is only a block away from my apartment!). On the first day of student orientation I rose earlier than normal. And as I arrived at the auditorium, I pushed through the doors with eyes beaming and bellowed a hearty “hello” to what awaited me on the other side. I was greeted with a flickering light and an empty room. This was when I came to realize that perhaps I was a bit overzealous in my arrival; I was over an hour early to the event and the sun had barely risen.
                Yet for the months to come, I aimed to face each day with the same degree of enthusiasm and fervor. As a newcomer at Roswell, I was well aware that my colleagues and superiors would be years ahead in terms of knowledge and experience pertaining to oncology. There were many aspects of the field I had yet to uncover and it was quite a shift. Although I had previously delved into cancer research, my primary training was in neuroscience. However, looking back I now realize that I was more than ready to face any challenge that was to come my way due to my years at the College of Staten Island.
During my time at CSI I had the honor of working with Dr. Probal Banerjee and his lab for several years.  One of the greatest assets at CSI, I realized, is the opportunity for students to work closely with faculty members and perform high-level research. I took advantage of this environment and along the way, I gained many skills through my involvement in various projects. For example, I was trained to record electrical activity of the hippocampus and prefrontal cortex with the aim of discovering effects elicited by drug-receptor interactions. I learned to work with cell lines, perform animal surgery, and synthesize drug compounds during my work in combating brain tumors. Equally as important, I was also taught how to think like a scientist, which involves the ability to analyze data while detecting the most minute of details, to assemble facts and form theories, and to question the prevailing dogma. This ultimately brought forth from myself a great appreciation for the sciences and it prepared me well for what was to come at the Roswell Institute.
I was then able to quickly integrate myself into my current lab environment at the Roswell Institute because of the mindset and practical skills I came armed with. Within the past few months, I have been able to further broaden my skills, allowing me to research prostate and pancreatic cancer as well as aging and genetic damage. I have been able to greatly expand my understanding of cancer biology, in terms of how it originates at the cellular level and what novel techniques are available for battling this disease.  And along the way, I have met some quite interesting personalities and made friends with some spirited individuals.

Going forward, I feel that I can make an impact on the world at large and make my dreams into a reality. And I will forever be grateful for the staff, colleagues, and friends at CSI who provided the lessons and experiences necessary for me to reach this point in my life. A life in which I am able to realize my passion and purpose.

Au Revoir France

Veronica LaManna, a member of the Verrazano Class of 2016 studying International Business with a minor in French, spent the Fall 2014 semester in Nice, France.  Returning home has given her time to reflect on the experience.

Returning back to the United States was extremely bittersweet.  I was so excited to see my family and friends again after four months, but so sad to leave the country that I was able to call home for those months.  In those four months I was able to experience so much through education and socialization.  Everyday I really learned so much in and out of the classroom.  As I stepped off the plane and back into New York I even experienced a little culture shock to hear everyone speaking English again.  I had been so accustomed to all the language barriers and picking up more and more everyday on the French language that my own first language sounded strange to me.  After being jet-lagged and freezing, due to the extreme climate change, for two weeks I am slowly getting used to life back here in New York.  It is good to be back, but I cannot begin to explain how much I miss living in Nice, and not just for the incredible weather.
            As soon as I returned home my family immediately wanted to see all 3,000 pictures I had taken while I was abroad.  While I was studying abroad, I was able to visit three different countries other than France.  As I talked about in previous blog, I had been to Morocco and Italy.  The last country I traveled to was Switzerland, which was another incredible experience.  I am so fortunate that I was able to see so much while I was abroad.  Studying abroad gives you the opportunity to travel to many countries while you are on a strict budget.  In Europe the flights are affordable and there are so many student discounts that are offered.  If I had not studied abroad I would have been less likely to have ever seen these countries.  I have made so many memories and have met so many amazing people during my travels, which makes me so happy that I took advantage of this opportunity. 
            While I was abroad, I began working on my research paper to graduate with honors in my major of international business. My educational experience in France highly encouraged my topic choice and my basis of information when I wrote my abstract.  Being able to study in an educational system that is completely different from the one that I am used to was the most challenging thing for me.  The challenge was definitely worth it because I learned so much from it. Studying abroad has taught me how to learn in an entirely different way.  I learned how to apply what I learn differently then how I would in my courses here.  Also after studying abroad the first time it gave me the idea to pursue my master’s degree in France. 

            Overall studying abroad was a positive and enriching experience.  I have so many memories and now have friends in almost every country.  I have grown and matured through this experience by living on my own, learning about different cultures, and meeting new people.  After coming back I really do not feel like the same person.  Now I am able to handle more responsibilities without stressing out as much.  I learned so much and I am so happy that I was able to have this incredible opportunity.  Nice will always have special place in my heart and will always feel like home. Jusqu’à la prochaine fois