| 摘要: | Despite the existence of several anomalous phenomena in capital markets research such as the small-firm and book-to-market effects, volatility smile seems to be the only major anomaly in options research. Two anomalous phenomena in the implied volatility function are that the risk-neutral distribution is more negatively skewed than the physical one, and that the index options exhibit more pronounced volatility smile than individual options. While investigating the related 「puzzle,」 some researchers indicate that volatility smile is related to systematic risk, a phenomenon being inconsistent with the Black-Scholes paradigm. But why is volatility pattern related to systematic risk? No satisfactory answer has yet been proposed to tackle this seemingly contradictory phenomenon. There are also several econometric and theoretical issues with the literature. Hence, this project shall contribute to the literature from both the econometric and theoretical aspects. First, we will discuss econometric problems with the existing literature, propose different model specifications, and compare the performance of the models in fitting the implied volatility curve via non-nested hypothesis tests. The existing empirical studies mostly adopt a single model specification (such as the double-log model or piecewise linear models) to fit the implied volatility curve, while ignoring that different types of options (such as the FX option) may exhibit different patterns. We propose the use of spline regression and Box-Cox models to allow for a wider range of functional relationship. While asserting that the implied volatility pattern is related to systematic risk, researchers only use the simplest market model, with S&P 500 index being the proxy for market portfolio. We propose using Fama-French three-factor model in the hope that the proposed model may provide better description of the systematic components of changes in the underlying stock returns. Second, there is a lack of complete investigation on volatility smile from behavioral viewpoints. As it is well documented that arbitrage is not unrestricted, researchers have tried to investigate if arbitrage risk plays a role in stock returns. Since arbitrage risk is of special importance in option pricing, it would be interesting to investigate if volatility smile is related to arbitrage risk. Recent capital markets research indicates that variables like BM and idiosyncratic risk matter, and may proxy for arbitrage risk. We conjecture that it is in fact the idiosyncratic risk, rather the systematic risk, that is related to implied volatility. We will investigate if there contains non-rational component in the volatility patterns. In particular, it is of interest to investigate if investor over/underreaction is related to volatility pattern. We shall adopt various behavioral factors such as sentiments to examine if behavioral factors can explain the pattern of volatility smile. We shall provide a complete investigation of the cross-sectional and timeseries properties of volatility patterns. We plan to investigate similar issues using a large cross-section of stock options to provide a more complete picture. 研究期間：9508 ~ 9607 |
