在現實生活中，無套利定價模型布雷克-休斯模型(Black-Scholes Model)下的假設如無交易成本、可連續時間交易等等的不符合現實的設定使得以此模型所定價出的選擇權價格實際上存在著套利空間。而Leland(1985)、Henrotte(1993)與Martellini(2000)等人分別發展出在time-based策略、move-based策略與diversified time-based策略以修正隱含波動率得到避險波動率的方法使得選擇權價格能夠涵蓋住複製選擇權所需的交易成本。 而在本文中與以往研究的不同是在於吾人加入了流動性風險成本一併做探討，來比較此三種策略在各種情境下的優劣，並以＂蒙地卡羅模擬修正法＂與Leland(1985)等人的方法做比較，吾人發現以蒙地卡羅模擬修正法所得到的避險效果與以Leland等人幾乎一樣，接者吾人便以此方法來修正考慮流動性風險成本與交易成本下的選擇權價格，並且也探討在未知真實股價報酬分配為隨機波動率模型(Stochastic volatility model )下誤以為股價報酬分配為布雷克-休斯模型假設，而使用Leland(1985)等人之修正法與蒙地卡羅模擬的修正方法之效果比較，以蒙地卡羅模擬結果發現即使在未知真實股價報酬分配下，所得的到避險效果也相當不錯。 根據吾人所比較之結果發現diversified time-based策略表現最佳，而move-based策略僅只有在低總成本且高波動率下表現較佳，一但總成本稍高時，表現便會非常不好。此結果不論在布雷克-休斯模型或是隨機波動率模型下都是一致的。 The assumptions of no-arbitrage Black-Scholes model, such as no transaction cost, time-continuously tradable, do not exist in real world and that make arbitrage possible. However, to make option price cover the transaction cost of replicating options, Leland(1985), Henrotte(1993) and Martellini(2000) have developed time-based strategy, move-based strategy and diversified time-based strategy, respectatively, by deriving hedge volatility revised from implied volatility to cover transaction cost. In relation to previous works, the major difference in this paper is that we encompass the cost of liquidity risk and we not only compare the various situations of these three strategies but also compare these outcomes that derived from “Monte Carlo simulation revised approach” with outcomes that derived from approaches of Leland (1985) etc. And we find the performance of “Monte Carlo simulation revised approach” is alike to performances of Leland(1985) etc. Then we use the approach to compute option price when considering liquidity risk cost and transaction cost,compare results of approach of Leland (1985) etc. and Monte Carlo revised approach under Stochastic volatility model is the true stock return process, and we find that the hedge effect by Monte Carlo simulation is good even if stock return true process is unknown.According to our comparison, diversified time-based strategies perform best whereas move-based strategies perform better only under low total cost and high volatility and move-based strategies perform extremely bad when total cost is just a little high.
