歐式保本型選擇權之設計與定價

本文針對投資人的保本心態，設計新奇選擇權，定名為保本型選擇權，將保本型選擇權定義如下：若買權（賣權）於觀察期限截止日，標的資產價格小於等於（大於等於）界限價格，則賣方退還買方原權利金並回收其流通在外的選擇權；若標的資涼價格大於於（小於）界限價格，則保本型選擇權等於一般型選擇權。應用平賭測度轉換，在利率隨機假設下，推導出股票、債券及股票交選擇權價格封閉式解。假設遠期利率波動度為債券到期期間之駝峰型函數，分別探討駝峰益、直線型與微笑型利率期間結構下整選擇權價格行為與避險比例變化。This study designs an exotic option called rebate option, which aims at the conservativeness of investors. The definition of rebate option is: if the price of underlying asset is smaller (larger) than the barrier price at the end of the monitoring period, then the writer will pay back the initial price of the rebate option to call the outstanding options; and if the price of underlying asset is strictly larger (smaller) than the barrier price at the end of the monitoring period, then rebate options will be equal to traditional options. By martingale methods, this study derives a set of closed-form pricing formulas including stock rebate option, bond rebate option, and stock exchange rebate option. Assuming that the evolution of the forward rates is based upon a deterministic and humped volatility function, this study discusses how the option price and the hedge ratio react when the pricing parameter changes, given different initial term structures of the interest rate.