An Empirical Analysis Of Option Pricing Under Jump Diffusion

JD model is an extension of BS model, added jump to the formula of the underlying asset price. Using Barndorff method of bipower variation can check the price of the underlying assets commonly exist jumps. And using the cumulant matching method proposed by Press, Becker, estimates jumping frequency put forward by Merton.We can find that an average of Poisson jump is 0.1650 on each trading day, a year jump number is 41.5895, an average of one jump is 6.0592 day. Therefore, JD model is considered to be a more realistic model than the BS model, need to take the factor of jump into consideration.Using the method of bipower variation to test the prices of assets exist jumps. According to this situation, this paper puts forward the Poisson jump diffusion model(JD) of Merton proposed and BS pricing model to make a comparative analysis. we estimate parameters of the jump diffusion model(JD) by using the cumulant matching method. And then, we empirically examine the pricing performance of the BS and JD models using daily closing prices or simulating daily closing prices of eight European options traded on Shanghai Stock Exchange, China Financial Futures Exchange and Hong Kong Stock Exchange. According to certain filtering rules and data processing, we get 27371 daily closing prices as the research sample. Empirical results show that the JD model is more realistic than the BS model, the effect of its pricing is better than the BS model, and both the two models underprice the options. At the same time, the trading activity of current option market is low, this relate to too much distribution of the depth in the money options and the depth out of the money options, so people want to buy the options distributing too little. The results can help the government and financial institutions make appropriate countermeasures scientifically, and thus promote the development of options market.