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

A basket option is another popular exotic option written on the value of a basket
(portfolio) of assets, and is actively traded both on exchanges and in over-the-counter
markets. Basket options are traded mainly for investing and hedging a portfolio of assets,
including stocks, stock indexes, currencies, and commodities. For example, if an investor

expects that there is a booming energy market in the near future, they can buy call options
on a basket of energy products, such as crude oil, natural gas, and their refined products.
Another example is that if a company has receivables in various currencies and worries

about adverse fluctuations of exchange rates that may reduce their domestic-currency
value, the treasurer may buy a basket put option on relevant currencies to hedge this risk.
The challenge of pricing and hedging basket/spread options mainly stems from the
lack of an explicit distribution of the sum/difference of correlated lognormal variates, and
thus, their closed-form pricing formulas and hedge ratios cannot be derived. Therefore,

to price basket/spread options, a variety of numerical methods and approximate pricing
formulas have been developed and extensively used in the marketplace. For basket
options, Levy (1992) approximates the underlying basket by the lognormal distribution

and matches the first two moments with the distribution of the underlying basket. Gentle
(1993) approximates the underlying basket by a geometric average, which relies on the fact
that the geometric average of the lognormal distribution is also lognormally distributed.
Milevsky and Posner (1998) apply the reciprocal gamma distribution and Posner and
Milevsky (1998) use the shifted lognormal distribution to derive the approximate pricing

formula of the basket options. Ju (2002) applies the Taylor expansion method; Flamouris
and Giamouridis (2007) use the Edgeworth expansion method, and Bae, Kang, and Kim
(2011) extend Ju's approximation (Ju, 2002) to derive the approximate pricing formula of

the basket options. Kan (2017) extends Levy (1992) by modifying the moment matching
approach to develop a Black-Scholes-type (Black and Scholes, 1973) formula. Moreover,
Rogers and Shi (1995), Carmona and Durrleman (2005), Xu and Zheng (2009), and
Caldana, Fusai, Gnoatto, and Grasselli (2016) derive the lower and upper price bounds of
the basket options. Bayer, Siebenmorgen, and Tempone (2018) and Choi (2018) focus on

the numerical quadrature integration technique that can ease the curse of dimensionality,
and numerical pricing results show that the pricing method is accurate and efficient.
For spread options, Shimko (1994) approximates the two asset spread option prices

by the expansion method provided by Jarrow and Rudd (1982). Kirk (1995) extended the

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