| Summary: | 碩士 === 國立臺灣大學 === 數學研究所 === 88 === A two-factor convertible bond is usually modelled by a parabolic partial differential equation
where V(r,S,t) be the price for a convertible bond, r is interest rate, S is asset price, the variable σ is the volatility of the stock price, u andω are the volatility of interest rate, ρis the coefficient which correlate of dZS and dZr, and λr is the market price of risk. It is usually puzzled to people what is the natural boundary condition at r=0 and r=ru, the minimum/maximum value of interest rate.
In this thesis, we show that, by energy method, when ω is degenerated at r=0 and r=ru, and > 0 at r=0 and < 0 at r= ru respectively, no boundary condition is needed at these points. A simple numerical method without any boundary condition has been shown to be stable. Numerical test has also justify this stability.
|
|---|
