均數復歸效果對選擇權投資組合下方風險的影響

Mean-Reverting Effect on Downside Risk of Derivatives

本文探討在停損策略下不同選擇權投資組合的風險。考量標的資產價格符合波動度均數復歸隨機變動的特性下，使用蒙地卡羅模擬法估計投資組合所面臨的下方風險。以台灣加權指數買權進行模型配適之模擬結果顯示: (1)標的資產價格與波動度過程的相關性為負。(2)歐式買權、數值買權、亞式買權和回顧型買權的理論價格由深價內到深價外遞減。(3)投資組合的下方風險由深價內、價平至深價外隨之增加。(4)歐式買權和亞式買權投資組合的下方風險大於數值買權和回顧型買權。(5)使用台灣指數的歷史資料搭配模擬，發現投資組合的回復率並沒有如Leoni (2008)的結果高，顯示使用停損策略對控制下方風險依舊有其必要性。

This study adds to the understanding of the risk of portfolios by exploring the impact of the stop-loss strategy. The Monte Carlo approach generates several interesting results. First, the correlation of price and volatility process is negative. Second, the downside risk of portfolios decreases monotonically with moneyness. Third, the downside risk of European call and Asian call are larger than digital call and lookback call. Finally, the empirical results show that the portfolios' recovery rates are not as high as Leoni (2008). It is important to control the downside risk through stop-loss strategy.