A study on the smile of TXO by arbitrage strategies

• Main Authors: Tsao Li-Chieh, 曹立杰
• Other Authors: Pan Ging-Ginq
• Format: Others
• Language: zh-TW
• Published: 2008
• Online Access: http://ndltd.ncl.edu.tw/handle/46256301898437180146

碩士 === 國立屏東科技大學 === 財務金融研究所 === 96 === B-S implied volatility is the volatility implied by the market price of the option based on Black-Scholes model. The importance of implied volatility is like the value of option for option contract. Real implied volatility curve is thought to be a horizontal line admittedly. If B-S model is correct and the market is efficient, implied volatility should be the same for the options with different strike prices. But B-S implied volatility curve presents the smile or smirk, generally called the smile phenomenon. The most popular explanation is that the smile reflects erroneous assumptions in the B-S model about the stochastic process of underlying assets price, and that is why they address themselves to construct the correct pricing model. But there is no pricing model which can purely explain the smile phenomenon until now. Other scholars thought that the inefficient market is the main reason for smile phenomenon so they inspect if the market is efficient or not by arbitrage strategies. This paper uses the daily data during January 2003 to December 2007 from TEJ, find that the implied volatility of TXO call presents smirk and the TXO put presents smile. Besides, the implied volatility of a call is obviously different from a puts with the same strike price. The B-S smile phenomenon does not mean that the smile phenomenon exists in real implied volatility curve because the B-S implied volatility is not equal to the real implied volatility. To inspect if the smile phenomenon exists in real implied volatility curve or not, given not to assume any stochastic process of underlying assets price, this paper develops four Delta-neutral arbitrage strategies depends on TXO B-S smile phenomenon. We implement arbitrage strategies by selling high implied volatility and buying low implied volatility to discuss the following topics: 1. If the B-S smile phenomenon is an illusion? 2. Why does TXO smile phenomenon not die out due to the arbitrage trade if the B-S smile phenomenon is not just an illusion? 3. Does TXO smile phenomenon result from inefficient market? The empirical results are shown as follows: 1. Before deducting the transaction cost, various arbitrage strategies profit is more than zero obviously. Representing that there are obviously differs of implied volatility between the call and put with the same strike price and also between the calls or puts with different strike prices. Furthermore, the differ of real implied volatility is more than what the B-S implied volatility represents, the B-S implied volatility is not an illusion. 2. The sustained existence of TXO smile phenomenon may be closely linked to the transaction cost. 3. The expensive transaction cost eliminates the gross margin of the arbitrage strategies, the TXO smile phenomenon does not result from inefficient market in consequence.