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see that most of the errors that we obtain by the simulation with the continuous model give the
better estimate than the model with jumps.

Table 1. The estimated parameters

The continuous model The model with jumps

ˆ  ˆ  ˆ  ˆ   
ˆ
ˆ
2
c c d d
Data 1 0.2764 0.2275 0.0011 0.0087 0.2049 0.0273
Data 2 -0.2921 0.5449 -0.0019 0.0041 0.2817 0.0678

Data 3 0.6515 0.2469 0.0027 0.0090 0.2279 0.0293

Data 4 -0.0431 0.3843 -0.0005 0.0115 0.1477 0.0593
Data 5 -0.0400 0.3240 -0.0004 0.0076 0.3317 0.0354

Data 6 -0.2614 0.2946 -0.0013 0.0074 0.5001 0.0257

Table 2. The average errors which are obtained by both models (%)

The continuous model The model with jumps
Data 1 14.94 16.07
Data 2 42.10 66.63

Data 3 20.61 39.84
Data 4 28.90 26.92
Data 5 22.02 22.83
Data 6 25.15 47.08

In the Table 1 we see that the estimated volatility ˆ  of the model with jumps is very
d
small. In the real market the volatility should not be small value. The typical value of volatility in
the real market should be around 15 % to 60 % (Hull and Options, 2000). For this reason we

change the estimation of ˆ  to be according to the real market by applying this simple
d
transformation

b  a  
ˆ      x   4 
a
d
 8 