絕對漲跌幅限制市場的選擇權評價

Abstract

在漲跌幅限制不存在時，Black-Scholes模型提出了一個合適的市場評價公式。在現實中，許多國家利用漲跌幅機制來穩定價格的波動。一般來說，我們會使用蒙地卡羅法來模擬出選擇權價格，但耗時卻是一個無法避免的代價。這也就是為什麼後來的研究都想找出一個解析解來評價選擇權，在準確度差距不大下，所需時間卻可大幅降低。本篇文章提出一個近似解析解，用來評價受到絕對漲跌幅限制的選擇權。根據模擬結果顯示，相對於解析解，Black-Scholes模型由於忽略了漲跌幅限制的條件，存在著過度評價的問題，容易失真。

The Black-Scholes formula describes a closed-form solution in the non-price-limit market. In reality, many countries use such price-limit mechanisms to stabilize prices. However, if we want to find out the price of options, we take into account the Monte-Carlo simulation method. But this option is time-consuming and further illustrates the importance of closed-form solutions. Therefore, this paper proposes a closed-form solution for pricing options in the absolute daily price-limit market. Based on the numerical results, the Black-Scholes formula has the problem of being overvalued until the price limit is relaxed.