Abstract: Swaps and pricing models in Financial Mathematics

Mentor: Dr. Leslie Cheng

Name: Zhuoman(Sophie) Zhao

Financial Mathematics is a field of applied mathematics concerned with lots of derivatives whose values depend on other index, interest rates and financial assets (e.g., options, the rights to buy or sell an asset such as a stock, oil, corn, etc.).

The focus of my research will be on swaps, in particular interest rate swaps and currency swaps. A swap is an agreement between two parties to exchange, or swap, future cashflows. In the interest rate swap, two parties exchange cashflows based on the interest rate: A pays B a fixed interest rate and B pays A a floating rate. Eventually the two parties are better off than before the swap. A currency swap is an exchange of interest payments between two currencies such as Australian dollars vs US dollars.

In addition, I will also examine derivatives such as options to gain a better perspective of swaps.

In Financial Mathematics, there are some classic mathematical models that can be used in investigating and supporting other ideas. In exploring the usage of swaps, I will look into some mathematical models, such as the Black-Scholes model and stochastic models (which estimate probability distributions of potential outcomes by allowing fluctuations observed in historical data, such as stock prices or interest rates).

Wilmott, P. (2007). Chapter 15. *Introduces Quantative financial Mathematics*(Edition 2., pp.357 ). UK: John Wiley & Sons, Ltd.