| Summary: | 碩士 === 東海大學 === 數學系 === 99 === There are two main topics in the present study. The first topic focuses on determining the parameters of the Vasicek model. Since if we use the zero coupon bond as a price model to pricing the option value, the simulation of term structure is very important. Before the bond price is obtained, we have to simulate the short interest rate using Vasicek model. The likelihood function is used to estimate the parameters of Vasicek model with U.S. Treasury one year bond rate data.
The asset price in the current market is modeled with Black-Sholes, and Merton construct a Poisson process into their model to describe if there are some extreme jumps in the asset price. The second part of present study is to estimate the parameters of Black-Scholes model and the jump-diffusion mode by using the maximum likelihood approach.
Keywords: Maximum likelihood, Black-Scholes model, jump-diffusion model
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