Interest Rate Model and Option Pricing

Open Access
Author:
Wang, Xinyu
Area of Honors:
Mathematics
Degree:
Bachelor of Science
Document Type:
Thesis
Thesis Supervisors:
  • Anna L Mazzucato, Thesis Supervisor
  • Sergei Tabachnikov, Honors Advisor
Keywords:
  • Financial Mathematics
  • Interest Rate Model
  • Black Scholes Model
  • Option Pricing
  • Compuational Finance
Abstract:
In the 2008 Financial Crisis, one of the primary sources causes this disaster is Mortgage- Backed Security(MBS), which is one of the derivatives among thousands. People who are un- familiar with finance would ask, what is derivatives? Derivative is a contract between two or more parties whose value is depended on an agreed-upon underlying financial products or set of assets. Financial institution developed derivatives aiming to creates tools for investors to hedge risks, but at the same time, hedging depends on accurately assuming risk. If financial institutions and in- vestors do not know how to use it in a right way, it may lead to catastrophe. Therefore, how to price options become an essential problem. There are two major underlying financial assets trading in the market, which are bonds and stocks. The bond market size is about $40.7 trillion and the stock market size is about $30 trillion in U.S., which means the stock options and bond options are major derivatives in the market to hedge risks. This paper focus exactly on these two options, which includes a view of the approach to the models and different methods to solve those models.