美式利率期权定价的抛物型变分不等式

A parabolic variational inequality arising from the valuation of American interest rate options

应用PDE方法对美式利率期权定价问题进行理论分析.在CIR利率模型下美式利率期权定价问题可归结为一个退化的一维抛物型变分不等式.通过引入惩罚函数证明了该变分不等式的解的存在唯一性,然后研究了自由边界的一些性质,如单调性,光滑性和自由边界在终止期的位置.

The valuation of American interest rate options is analyzed theoretically using a PDE method.Under the assumption that interest rate obeys the CIR model,the valuation of American interest rate options can be formulated as a one-dimensional degenerate parabolic variational inequality. The existence and uniqueness of the solution of the variational inequality are proved using a penalty function.Some properties of the free boundary are studied,such as monotonicity,smoothness and the location of the free bounda...