- 期刊
以套利策略探討臺指微笑現象
A Study on TAIEX's Smile by Arbitrage Strategies
摘要
若市場具有效率且模型正確，則隱含波動度不應隨履約價格而有顯著差異。本研究以Black-Scholes model計算2005年至2012年的臺指隱含波動度，發現：（1）相同履約價之價內買權隱含波動度高於價外賣權，差異程度於2008年9月爆發金融海嘯後獲得緩解；（2）臺指選擇權確實存在微笑現象。依據臺指微笑現象，且遵循買入低BS隱含波動度、賣出高BS隱含波動度選擇權為原則，本研究模擬四種Delta-neutral套利策略。藉由套利利潤的統計分析，探討（1）臺指選擇權是否違反put-call parity？（2）臺指微笑現象是否只是假象？（3）臺指微笑現象是否隨市場漸趨成熟而消失？（4）微笑現象是否意味市場無效率？本研究方法的優點在於（1）免除模型設定問題，（2）可以釐清微笑原因究竟為市場無效率或BS model錯誤。實證結果如下：（1）臺指選擇權違反put-call parity，（2）臺指微笑現象並非假象，（3）隨著市場的愈臻成熟，違反put-call parity的程度與微笑現象皆獲得改善，（4）持續存在的微笑現象並非肇因於市場無效率。
並列摘要
If a market is efficient and a model is correct, then there is no difference between implied volatilities with different strike prices. Based on the Black-Scholes model and using a TAIEX options data set during the period from year 2005 to 2012, this study discovers: (1) with the same strike price, in-the-money call's (put's) implied volatilities are higher than those of out-the-money put (call); (2) the shape of implied volatility curve is like ”smirk”. According to TAIEX's smile and obeying the rule: buying options with low BS implied volatility and selling options with high BS implied volatility in Delta-neutral portfolios, this paper develops four arbitrage strategies. By analyzing the statistical properties of profits to trading strategies, this paper discusses the following subjects: (1) whether the put-call parity is violated, (2) whether the true implied curve is flat, (3) whether TAIEX's smile relaxes as the market matures gradually, and (4) whether the persistent smile means the market is inefficient. Two advantages of our methodology are: (1) it does not require specification and testing of an alternative to BS, (2) it can clarify that the smile is due to erroneous assumptions in the BS model or the market inefficiency. The empirical study shows the following results: (1) the TAIEX option violates the put-call parity, (2) the true implied curve does not be flat, (3) TAIEX's smile relaxes as the market matures, and (4) the persistent smile is not due to the market is inefficient.