On the approximation to the optimal rigion

点击翻译按钮获取中文摘要

We considered new type of barrier type options. Unlike the ordinary barrier options, which have either straight line or constant barrier in terms of the underlying Brownian motion, our barrier is proportional to the square root of the time (Exponential Square root Barrier Knockout Option). Since the fluctuation of Brownian motion is proportional to the square root of the time, our barrier is more natural than the others. We have used the results of Siegmund (1985) and Morimoto (1999) for calculating the necessary probabilities. In addition to the above, we have also considered the discrete time version of the Exponential Square Root Barrier Knockout Options. We have used the asymptotic expantion for the non-linear renewal theorem given by Takahashi-Woodroofe (1981, 1982) for calculating necessary conditional probabilities. The extentons to American type option may be obtained by combining our result with Aitsahilia-Lai (2000), the final result is yet to come though.