Modeling The Implied Volatility Based On Hongkong Stock Option

The Black-Scholes model played an important role in option pricing theory. When it wasestablished, it assumed volatility to be constant.However, more and more examples haveproved this assumption in real market is incorrect.Actually, the implied volatility versus strikeprice shows a “smile” shape when maturity is fixed.And, it will show some maturity structurecharacteristics when the strike is fixed. The implied volatility,strike and maturity make up a3D graphics,which is so-called "volatility surface".This surface contains a lot of informationof the option contract,thus becomes the important tool for option analysis and pricing.Modeling the implied volatility surface has been a hot research topic in the field offinancial quantitative economic.Common methods of modeling include the parametric model,non-parametric model and semi-parametric model.Although parametric model is simple, iteasily leads to large deviation since it always requires a fixed style between thefactors.Non-parameter model can be used in a variety of shapes, but it works only if theamount of data was satisfied. Semi-parametric model is widely applied because it overcomesthe shortcoming of the former.We discussed the three models above and made a comparisonof them. We do some modifications based on the original models and get the new models atthe same time.The improved modelsare more flexible and simple, thus is much closer to theactual application.The market of Hongkong stock option is the most active one in Asia-Pacific region.Nevertheless,the research of implied volatility based on Hongkong stock option is ignored.This paper is to research the implied volatility of Hongkong stock option based on originalmodels and improved ones.First we select the data of HSBC option and divide it into twoparts according to the time. One part is used for fitting models.Another part is used for testingthe forecasting ability of the models. At last, we get two conclusions.First,the improvedmodels have a better fitting and forecasting ability. Secondly, the improved model can be wellapplied to the market of Hongkong stock option.