Volatility long memory is a stylized fact that has been documented for a long time. Existing literature have two ways to model volatility long memory: component volatility models and fractionally integrated volatility models. This paper develops a new fractionally integrated GARCH model, and investigates its performance by using the Standard and Poor’s 500 index returns and cross-sectional European option data. The fractionally integrated GARCH model signi?cantly outperforms the simple GARCH(1, 1) model by generating 37% less option pricing errors. With stronger volatility persistence, it also dominates a component volatility model, who has enjoyed a reputation for its outstanding option pricing performance, by generating 15% less option pricing errors. We also con?rm the fractionally integrated GARCH model’s robustness with the latest option prices. This paper indicates that capturing volatility persistence represents a very promising direction for future study.

This paper explores whether the pricing of the option-type derivative is affected by some of fundamental characteristics, such as size and liquidity of the derivative itself and the underlying asset, which are not involved in the standard pricing theory. Considering the unique status of warrants in China due to the relatively more flexible trading mechanism, I empirically examine the pricing of Chinese covered warrants to develop this study. Empirical results show that market prices of Chinese warrants are significantly higher than theoretical prices predicted by traditional pricing models such as Black-Scholes, Jump-Diffusion, and CEV model. For call warrants, about 25 percent of the market price can not be explained by pricing models, and this figure rises to over 60 percent for put warrants. Further regression tests show that both size and liquidity of warrants and underlying stocks significantly affect warrant pricing errors. The way in which the size and liquidity affect the pricing error depends on the type of warrants. In addition, it is evident that movements of put warrant prices in China do not follow movements of stock prices. To explain the above pricing puzzles,the concept of functional asset pricing is proposed. According to this concept, these pricing puzzles just reflect the existence of functional value of financial instruments that has long been neglected by traditional pricing models. In fact, Due to the high level of liquidity and popularity, the Chinese warrant may well function as a good tool for obtaining short-term profits. The pricing of Chinese warrants by the market may correctly re°ect the value of this function, and thus is rational in essence.

This paper provides an in-depth analysis of the Hansen-Jagannathan (HJ) distance, which is a measure that is widely used for diagnosis of asset pricing models, and also as a tool for model selection. In the mean and standard deviation space of portfolio returns, we provide a geometric interpretation of the HJ-distance. In relation to the traditional regression approach of testing asset pricing models, we show that the HJ-distance is a scaled version of the aggregate pricing errors, and it is closely related to Shanken’s (1985) cross-sectional regression test (CSRT) statistic, with the only major dierence in how the zero-beta rate is estimated. For the statistical properties, we provide the exact distribution of the sample HJ-distance and also a simple numerical procedure for computing its distribution function. In addition, we propose a new test of equality of HJ-distance for two nested models. Simulation evidence shows that the asymptotic distribution for sample HJ-distance is grossly inappropriate for typical number of test assets and time series observations, making the small sample analysis empirically relevant.