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

Table 1 The GB Parameters of Each Numerical Example Provided in Borovkova
et al. (2007)
Terms GB1 GB2 GB3 GB4 GB5 GB6
S i (0) [100, 120] [150, 100] [110, 90] [200, 50] [95, 90, 105] [100, 90, 95]
[0.2, 0.3] [0.3, 0.2] [0.3, 0.2] [0.1, 0.15] [0.2, 0.3, 0.25] [0.25, 0.3, 0.2]
σ i
[-1, 1] [-1, 1] [0.7, 0.3] [-1, 1] [1, -0.8, -0.5] [0.6, 0.8, -1]
α i
ρ 1,2 = ρ 2,3 = 0.8 ρ 1,2 = ρ 2,3 = 0.8
ρ 1,2 = 0.9 ρ 1,2 = 0.3 ρ 1,2 = 0.9 ρ 1,2 = 0.8
ρ 1,3 = 0.8 ρ 1,3 = 0.8
ρ i,j
K 20 -50 104 -140 -30 35
T 1 1 1 1 1 1
Note: The notations are defined as follows: S i (0): the initial asset price; σ i : volatility; α i : units of the ith
asset; ρ i,j : correlation coefficient between S i and S j ; K: strike price. The dividend yield rates of
all assets are assumed to be zero, namely, q i = 0 and the risk-free interest rate, r, is assumed
to be 0.03.
Table 2 The Numerical Examples of GB Options Provided in Borovkova et al.
(2007)
Method GB1 GB2 GB3 GB4 GB5 GB6
USD 7.739 16.767 10.824 1.958 7.740 9.009
BPW 7.751 16.910 10.844 1.958 7.759 9.026
MC 7.744 16.757 10.821 1.966 7.730 9.012
se 0.014 0.023 0.018 0.005 0.010 0.015
Note: This table presents the pricing results of various GB options computed by three different
approaches: USD represents the pricing model proposed in this article, BPW represents
the pricing model presented in Borovkova et al. (2007), and MC denotes the Monte Carlo
simulation method. The standard error of Monte Carlo simulation is denoted by se.
and Cathay Financial Holdings Co., Ltd. (2882). The market data of the representative

companies include the stock price and dividend yield within the period from January 1,
2020, to August 31, 2022, and all data are from the Taiwan Economic Journal.
Assume that the valuation date is August 1, 2022; then, the initial stock of each
company is S 2330 (0) = 505, S 2603 (0) = 88.3, and S 2882 (0) = 44.55. The average yield of

each company during this time period is q 2330 = 2.1%, q 2603 = 3.5%, and q 2882 = 4.8%. The
strike price is assumed to be in-the-money. The historical volatility of each company is
computed by the annualized standard deviation of stock return, which are σ 2330 = 27.4%,
σ 2603 = 65.8%, and σ 2882 = 24.1%, respectively. The historical correlation coefficient

between companies is calculated by the Pearson's correlation method, which are ρ 2330,2882 =
45.1%, ρ 2603,2882 = 34.0%, and ρ 2330,2603 = 17.1%, respectively. The risk-free interest rate, r,

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