均數復歸效果對衍生性金融商品下方風險的影響

本文採用Leoni (2008)的方法探討在停損策略下不同選擇權投資組合的風險。使用台灣加權指數買權進行模型配適，發現Heston模型較B-S模型有較好的訂價績效，表示標的資產價格比較符合Heston假設下的均數復歸隨機波動過程。我們利用蒙地卡羅法模擬標的資產的價格服從均數復歸隨機波動，並進行Heston參數對下方風險的敏感度分析。依照不同買權類型和不同買權的價內外程度共組成25種投資組合。本文結果顯示：(1)買權投資組合的下方風險與買權履約的可能性相關，下方風險由深價內、價平至深價外隨之增加。(2)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。 (3)資產價格與波動度過程的相關性為負，買權投資組合有較小的下方風險。波動度過程中均數復歸強度和波動度的變動對買權投資組合下方風險的影響相反。對不同價性下的買權投資組合下方風險的影響結果呈現不一致。整體而言，透過選擇標的資產來降低買權投資組合下方風險的方法，只有在部分投資組合中才有較明顯的效果。(4)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，使用停損策略對控制下方風險依舊有其必要性。

關鍵字

衍生性金融商品；投資組合；下方風險；均數復歸；停損策略

並列摘要

This article documents the risk of different options portfolios under the stop-loss strategy proposed by Leoni (2008). We use the model to fit the call options on the TAIEX, and finding Heston outperforms the B-S model. It means that the underlying is agreeable with Heston's assumption to mean-reverting stochastic volatility. We carry out a Monte Carlo simulation of underlying with mean-reverting, and analyzing the sensitivity of downside risk to Heston parameter values. Depending on different classes of options and moneyness, the 25 portifolios have been formed. The results show that: (1) The downside risk of portfolios and probability of calls excercise are correlative, and downside risk decreases monotonically with moneyness. (2)The downside risk of Call options portfolio of European and Asian are larger than digital and lookback due to excercise style. (3)If the correlation of price and volatility process is negative, the downside risk of option portfolio will be smaller. The changes of mean reversion and volatility of volatility process to impact on downside risk are inverse and inconsistent under different moneyness call portfolios. Overall, selection of underlyings have been able to reduce portfolio’s downside risk on certain forms but not the others. (4)Simulations with Taiwan Index historical data, the portfolios' recovery rate aren’t as higher as Leoni (2008). It is useful to control of downside risk through stop-loss strategy.