Based On The Jump - Diffusion Model Of Open-end Fund Rate Study

The fixed rate system in open-end funds lacks the pricing mechanism. It is unfair to investors and difficult to create incentives for fund managers, because it is not linked with investment return, investment risk and some other factors. To solve these problems, this paper used the option pricing theory to study the management fee pricing mechanism of open-end funds. This paper applied Jarque-Bera normality test to the return series of all open-end funds in the sample from January 4,2007 to December 31,2010, and found all of them rejected the original assumption of normal distribution, so the B-S model which was used in previous paper is unreasonable, we can assume that some of the open-end funds'return series are subjected to jump-diffusion process. This paper gave the management fee formula under the minimum income goal and the double-limit income goal based on the option pricing formula of Merton jump-diffusion model. In order to obtain estimators of the parameters, this paper followed an idea that find jump first and then estimate parameters, took advantage of the jump-diffusion process's characteristics and the excluding method of abnormal values, proposed a new estimation for the jump-diffusion model. The simulation indicates that the method is applicable to both the jump-diffusion models and the estimators are ideal overall.The empirical analysis showed that:compared with the B-S model, jump-diffusion model can better reflect the right-skew and the peak of original data, the probability density curve of jump-diffusion model is closer to the original sequence, so it was reasonable to assume that some of the open-ended funds'return series obey jump-diffusion process. This paper set a standard that the jump range is significantly not equal to zero and selected 42 equity funds and 16 bond funds from the sample as the ultimate object of study. The estimation of parameters showed that the annual return,volatility and down-jumping range are relatively large, the bond funds is a relatively stable investment products. This paper argued that the management fee under the minimum income goal is unreasonable, and therefore proposed two double-limit income goal:0～8% and 2.25%～8%. Under the 0-8% target, the average optimal management fee of the equity fund is lower than the current rate, the average optimal management fee of bond funds is approximately equal to the current rate. The average optimal management fee under 2.25%～8% target is relatively high. This paper analyzed the expected return of investors and fund managers, found that the optimal management fee under double-limit income goal can not only guarantee investors a minimum income, but also encourage fund managers to pursue higher investment perfomance. As this pricing mechanism is fair to both sides and associated with the investment income and investment risk, so it is a good improvement of the fixed rate system.