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

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be used to price and hedge both options. For American basket and spread options,
Borovkova, Permana, and van der Weide (2012) develop an integrated pricing method via
a binomial tree model.
Numerical examinations show that the BPW model (Borovkova et al., 2007) can

accurately and efficiently price both basket and spread options in most cases, but its
accuracy decreases gradually with increasing volatilities, decreasing correlations among
underlying assets, and increasing time to maturity. This phenomenon can be explained

by the fact that the LS distribution has only three flexible parameters to fit the target
distribution. Thus, the BPW model (Borovkova et al., 2007) cannot well capture the high-
moment features of the target distribution and may cause some pricing error in some
extreme situations.
This study aims to extend and improve the BPW model (Borovkova et al., 2007)

by including the fourth parameter to approximate the target distribution. We adopt
the unbounded-system (US) distribution of the Johnson (1949) distribution family to
approximate the target distribution. The US distribution has four flexible parameters,

which can help in better capturing the high-moment features of the target distribution even
in the cases of high assetsʼ volatilities, low correlations among underlying assets, and
long time to maturity. Therefore, our resulting pricing formula can price both spread and
basket options more accurately in these extreme cases. Besides improving model accuracy,
the resulting pricing model is also derived in a closed form; thus, this model remains

computational efficiency. Moreover, their Greeks can also be derived analytically, which
helps market practitioners manage risks efficiently for both basket and spread options.
The rest of this article is organized as follows. Section 2 presents the market model,

and introduces the Johnson (1949) distribution family and their relevant properties. The
pricing formulae and their Greeks within the US-distribution framework are derived
in Section 3. Section 4 provides some numerical studies to demonstrate the model
implementation and examine the accuracy of the resulting pricing model. The conclusions
are presented in the last section.

4 Chang, Chen, and Wu (2012) provide the analytical solution for the equation system of the moment-
matching method presented in Borovkova et al. (2007).

5