依價格調整之Delta避險策略

A Price-Based Delta-Hedging Strategy

Delta避險策略是選擇權避險策略中廣泛應用的一種方法，用以降低持有選擇權部位的風險。在動態的策略當中，整體部位必須不間斷的重新平衡，大幅增加了交易成本。本研究在Black-Scholes模型下開發一種以價格為調整基準的Delta避險策略，推導出必須調整資產組合的價格區間，並證明在特定情況下，價格區間必定存在。我們亦應用蒙特卡羅模擬和實際資料比較以價格為調整基準和固定時間調整資產組合的Delta避險策略，模擬和實證結果均發現以價格為調整基準的策略可顯著降低交易成本。另外，我們將股價和波動度之間的負向關係納入實證考量，此為文獻中首例，發現以價格為調整基準的Delta避險策略在考量該負向關係之後，避險績效並無顯著改善。

Along the option-hedging dimension, the delta-hedging strategy is widely used to reduce the risk when holding a position in an option. Under a dynamic strategy, wealth must be rebalanced continuously, which significantly increases the transaction costs. In this paper, we develop a price-based delta-hedging strategy under the Black-Scholes model. We present the conditions used to derive the price band and prove that under such conditions, the price band always exists. To demonstrate the effectiveness of the price-based delta-hedging strategy, we first apply the Monte Carlo method to compare our price-based strategy with a time-based strategy. Furthermore, we empirically demonstrate that the price-based delta-hedging strategy significantly reduces the transaction costs. However, embedding the negative relationship between equity price and volatility in the price-based delta-hedging strategy does not significantly improve the hedging performance.