隨機利率下選擇權訂價模型

Abstract

Under Gaussian HJM framework, the first goal of the research is to derive the closed-form solution of market-traded contingent claims, such as Taiwanese capped options and under Gaussian HJM framework. I provide the closed-form solutions of generalized capped options (one of the special cases is Taiwanese capped options). However, some contingent claims do not have closed-form solutions, such as long-dated American stock options. Thus, how to develop numerical techniques such as lattice method and Monte Carlo simulation under Gaussian HJM framework is also important for option pricing. The second goal of the research is to provide the numerical methods such as lattice method, and Monte Carlo simulation under Gaussian HJM framework. Unlike the other numerical methods under stochastic interests, our methods can be used to compute the prices of equity derivatives which are related to interest rate, for example, long-dated American stock options.