C. Fitting analysis for partial distribution.

The methods of estimating the parameters is from 2) in appendix.

1) The fitness of DJX. We take the close points of 1/100DJ INDU as sample data. Time: Jun. 19, 2002 -Dec. 24, 2002. Trading days: n=132. Length of each field: ∆=0.862121 2120.

Number of fields: m=25. The estimated results of parameters are as follows:

● The parameters estimated in partial distribution P( µ,σ² ) :

● The parameters estimated in lognormal distribution Ln ( µl , σl²):

● The fiducial test:

2) The fitness of MSFT. We take the close prices of MICROSOFT CP as sample data. Time: Jan. 29, 2002-Dec. 24, 2002.Trading days: n=230. Length of each field: ∆=0.467609(US $).

Number of fields: m=46. The estimated results of parameters are as follows:

● The parameters estimated in partial distribution P( µ,σ² ) :

● The parameters estimated in lognormal distribution Ln ( µl , σl²):

● The fiducial test:

D. Comparison research between DF pricing and BS pricing

Suppose r (risk-free rate of interest) =0.07. Here we compare results from DF formulas with those of BS (Black-Scholes) formulas in options pricing.

1) The comparative analysis for DJX. Time: Dec. 24, 2002 Product: The option contract on DJX Maturity: Expires After: Fri 19-Dec-2003. Underlying: Close point of DJX at current date, 84.48.

In table 1, the prices are of Dec. 24, 2002, which were the closing prices traded actually in the United States option market (TP), the call and put options prices calculated by DF pricing formulas, (DF), and the call and put options prices calculated by BS pricing formulas, (BS). From table 1, we see the DF prices are closer to the actual trading prices than the BS prices.

If taking the strike price, Z=88, and T=199 for example, the variety of call and put option prices calculated by DF formulas and BS formulas are respectively shown in figure 2(a) and 2(b).

Figure 2. Comparison between curves of options prices of DJX

2) The comparative analysis for MSFT. Time: Dec. 25, 2002. Product: The option contract on MSFT. Maturity: Expires After: Fri,16-Jan-2004. Underlying: Close price of MSFT at current date, 53.39$.

In table 2, there are the prices on Dec.24, 2002, which were the closing prices traded actually in the United States option market (TP), the call and put options prices calculated by DF structure formulas, (DF) , and the call and put options prices calculated by BS formulas, (BS).

According to the data from table 2, it is difficult to know whether the DF formula is better than BS formula or not, we should do further empirical research. Taking the strike price, Z=50, and T=212 for example, the variety of call and put option prices calculated by DF formulas and BS formulas are respectively shown in figure 3(a) and 3(b).

Figure 3. Comparison between curves of options prices of MSFT

In the table 1 and table 2, we can see that most of the prices calculated from DF formulas are more near to real options prices (TP) than those from BS calculated formulas.

E. Possible researches on following topics

1) Price analysis for other kind of derivatives.
2) Structure analysis for disk distribution.
3) Estimating analysis for worth of manpower.
4) The analysis and decision for the comparison construction of the foreign exchange rate.
5) Structure and characteristic analysis for credit grade.
6) The diaphaneity analysis for information of commodity.
7) Analysis for the degree of happiness and its distribution.
8) Structure and characteristic analysis for society health status.
9) Composing and distribution analysis of society potential power.
10) Structure and characteristic analysis of society moral behavior.

Prof. Feng Dai

Next: Acknowledgement and References

Summary: Index