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

where is defined in equation (4), , , and and
are given in equations (17)-(20).
With inheriting from the merits of the BPW model (Borovkova et al., 2007), the
derived pricing models given in equations (27) and (28) can together price both basket

and spread options, and thus, the pricing and hedging of the two options can be managed
consistently and efficiently. Furthermore, the pricing models improve the pricing capacity
of the BPW model (Borovkova et al., 2007) by incorporating one more flexible parameter,

which can capture the features of the first four moments of the GB distribution. Therefore,
the resulting pricing models can significantly reduce the pricing error, especially in the
situations of higher asset volatilities, lower correlations among underlying asset prices,
and a longer time to maturity.

resulting pricing models can significantly reduce the pricing error, especially in the situations of higher asset
3.3 Hedging Ratio
volatilities, lower correlations among underlying asset prices, and a longer time to maturity.
Hedging the GB options is as important as pricing them for investment banks.
Therefore, this subsection examines how to compute the hedging ratios (or the Greeks)
3.3. Hedging Ratio
of the GB options. Note that though the pricing formulas given in equations (27) and (28)
Hedging the GB options is as important as pricing them for investment banks. Therefore, this subsection
are presented in a close form, their Greeks cannot be analytically derived because
examines how to compute the hedging ratios (or the Greeks) of the GB options. Note that though the pricing
and must be computed via the Newton-Raphson method. To overcome this obstacle,
formulas given in equations (27) and (28) are presented in a close form, their Greeks cannot be analytically
this subsection suggests that the end-users should compute the Greeks directly by their
derived because �, , ̅, and must be computed via the Newton-Raphson method. To overcome this obstacle,
̅
�
definitions. For demonstration, the definitions of Greeks are presented as follows.
this subsection suggests that the end-users should compute the Greeks directly by their definitions. For
Definition 2. The Greeks of the GB options can be approximately computed by the
demonstration, the definitions of Greeks are presented as follows.
Definition 2. The Greeks of the GB options can be approximately computed by the following formulas:
following formulas:
( (0) + ) − ( (0))
�
�
��� = , ,
�

��� ( (0) + ) − ��� ( (0))
��� � � � � , ,
� =

( + ) − ( )
�
�
��� = , ,
�

� �,� + � − � �
�,�
��� = , ,
�,�

( + ) − ( )
, ,
=

( + ) − ( )
, ,
=

and
( (0) + ) − ( (0))
�
�
��� = 17 ,
�

��� ( (0) + ) − ��� ( (0))
�
�
��� = � � ,
�

( + ) − ( )
�
�
��� = ,
�

� + � − � �
��� �,� �,�
= ,
�,�

( + ) − ( )
���
= ,

( + ) − ( )
���
= ,

where is a sufficiently small number and the other parameters are fixed as a constant in the computation of
each Greek.
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