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NTU Management Review Vol. 34 No. 1 Apr. 2024

4.1 Numerical Examinations
Borovkova et al. (2007) adopt the LS distribution of the Johnson distribution family
to derive a versatile pricing formula which can accurately and efficiently price both the
basket options and spread options. However, our numerical examination below reveals that

the BPW model (Borovkova et al., 2007) yields relatively higher pricing errors in cases
of higher asset volatilities, lower correlations among underlying assets, and longer time
to maturity. To improve the pricing capability, this study adopts the US distribution of the

Johnson distribution family to approximate the GB distribution.
To examine the accuracy of our model, we first employ the numerical examples
provided in Borovkova et al. (2007) and compare the results computed via the BPW
model (Borovkova et al., 2007) and our pricing model. Table 1 presents the market
scenarios provided in Borovkova et al. (2007), and the pricing results are given in Table 2.

Clearly, our model yields almost the same prices as those computed from the Monte Carlo
simulation, while the BPW method (Borovkova et al., 2007) shows slight deviations from
the Monte Carlo simulation.

Note that the six market scenarios provided in Borovkova et al. (2007) are composed
of low volatilities and high correlations among the underlying assets, and short time to
maturity. Under these conditions, the BPW approximate pricing formulas (Borovkova et
al., 2007) easily perform well. However, our pricing formulas can accurately price the GB
options even in difficult situations, such as high volatilities and low correlations among

the underlying assets, and longer time to maturity. To support our claim, we provide more
comprehensive numerical examples and show that our model can deal with these difficult
situations better than the BPW model (Borovkova et al., 2007). The results are presented

in Tables 3, 4, 5, 6, 7, and 8.
Lo et al. (2014) adopt a shifted reciprocal gamma distribution to approximate the
distribution of the sum of lognormal variates. Therefore, this study also uses the same
approximation method to derive the pricing formulas of the general basket options and
their pricing results are also presented in Tables 3, 4, 5, 6, 7, and 8.

To evaluate the performance of each model by comparing it with the result computed
based on the Monte Carlo simulation method, we provide the percentage pricing error
(PPE), root of mean squared error (RMSE), and maximum absolute error (MAE), which

are computed as follows:

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