交易成本及漲跌幅限制下認購權證之最適避險策略

Abstract

根據傳統的Black-Scholes世界，在delta避險下，只要連續不斷調整避險比率，那麼就可達到無風險投資組合的境界。但是實務上，由於交易成本的存在，連續不斷的調整避險比率似乎不大可行。所以在間斷避險下，由於gamma風險的存在，投資組合便存在避險誤差。交易成本和避險誤差似乎存在兩難。如果常常調整避險比率，雖然可以降低避險誤差，但交易成本卻增加；反之，減少調整避險比率次數雖然可以降低交易成本，但卻會大幅升高避險誤差。券商如何在這中間取得平衡，乃是重要課題。另外，由於台灣股票市場有每天7%的漲跌幅限制，在有漲跌幅限制下，股價的分配不再是標準的對數常態分配，也因此傳統的Black-Scholes定價公式是否適用，也是個重要課題。如何調整B-S模型使能適用於台灣權證價格，也是重要課題。本研究的主要目的在推導出在交易成本及避險誤差兩難下，最合適的避險策略，另外本研究也嘗試再加入漲跌幅限制條件，最適避險策略該如何修訂，本文也應用Monte-Carlo Simulation的方法模擬避險策略的績效。

According to the traditional Black-Scholes world, the risk-free portfolio can be achieved by continuously adjusting the hedge ratio (delta-neutral hedge). However, in a real world, the transaction costs invalidate the Black-Scholes arbitrage argument for option pricing, since continuous revision implies infinite trading. The infinite trading will induce a huge amount of transaction costs. Hence, the hedgers are in dilemma. They face the trade-off between the transaction costs and the hedge error that occurs from the discrete revision. The purpose of this project is to develop an optimal hedging strategy for security firms that issue the call warrants. The regulation of 7% price limit on Taiwan stock prices is also taken into account for setting the hedging strategy. The Monte Carlo simulation approaches are used to compare the performance of different hedging strategies.