A parabolic variational inequality arising from the valuation of strike reset options
A parabolic variational inequality arising from the valuation of strike reset options
复制标题
DOI：
10.1016/j.jde.2006.07.026
复制
发表时间：
2006-11
影响因子：
2.4
通讯作者：
Zhou Yang;F. Yi;M. Dai
中科院分区：
文献类型：
--
作者：
Zhou Yang;F. Yi;M. Dai
执行重置期权是一种允许其保持器持有人在保持器选择的时刻将执行价格重置为当前标的资产价格的期权。期权定价模型可以表示为一维抛物型变分不等式，或者等价地表示为一个自由边界问题，其中自由边界恰好对应于期权保持器所采用的最优重置策略.本文对该模型进行了理论分析。证明了解的存在唯一性。此外，我们还研究了自由边界的性质。证明了自由边界的单调性和C∞光滑性.
A strike reset option is an option that allows its holder to reset the strike price to the prevailing underlying asset price at a moment chosen by the holder. The pricing model of the option can be formulated as a one-dimensional parabolic variational inequality, or equivalently, a free boundary problem, where the free boundary just corresponds to the optimal reset strategy adopted by the holder of the option. This paper is concerned with the theoretical analysis of the model. The existence and uniqueness of the solution are established. Furthermore, we study properties of the free boundary. The monotonicity and C∞smoothness of the free boundary are proven in some situations.