Comparisons between the Monte Carlo method and Finite Difference method for option price and interest rate models
Open Access
- Author:
- Wu, Jiawei
- Area of Honors:
- Mathematics
- Degree:
- Bachelor of Science
- Document Type:
- Thesis
- Thesis Supervisors:
- Anna L Mazzucato, Thesis Supervisor
Xiantao Li, Thesis Honors Advisor - Keywords:
- Numerical Analysis
Financial Mathematics
Partial Differential Equations - Abstract:
- In our daily life, we often see some financial news in which we will know the stock indexes such as the Nasdaq Index and the Dow Jones Index, as well as the current situation of the financial market. It can be said that the financial market is closely related to people's life. In March 2020, affected by the epidemic, three circuit breakers' historical occurrence in a short period in the US stock market also made people pay more attention to the financial market. So what are common things in financial markets? Financial markets are places where all kinds of financial instruments are traded, including stocks, bonds and so on. These financial instruments give rise to financial derivatives. One of the topics this thesis will discuss is options, which is also one of the financial derivatives. One of the most important and frequently discussed issues with options is how to price them. We often use various financial models to price options such as Black-Scholes model, CEV model and CIR model. In this thesis, we price European Call options using Black-Scholes model as well as two local volatility models, the Constant Elasticity Variance (CEV) model and the Cox-Ingersoll-Ross (CIR) model. The thesis will also talk about interest rate models and we will use interest rate models to price bonds. Specifically, the CIR model is also used to price bonds under stochastic interest rates. On the whole, this paper will first introduce the Monte Carlo method, Explicit Euler method and Implicit Euler method, then solve the option/bond pricing models' partial differential equation(PDE) using these three methods. Finally, there will be some comparisons between the three methods' accuracy under different circumstances and we will determine which one will get the most accurate solution.