Page 12 - 34-1

Valuation of Spread and Basket Options

closed-form pricing formula for exchange options proposed by Margrabe in 1978 to derive
an approximation pricing formula for two-asset spread options. Poitras (1998) uses the
Bachelier approximation to approximate the price difference of the two assets directly as a
normal variable and derives the pricing formula of spread options. Alexander and Scourse

(2004) apply the bivariate normal mixture model to approximate the underlying spread
and derive the approximate pricing formula. Li, Deng, and Zhou (2008) provide the price
bounds for digital spread options and derive the approximate pricing formula of spread

options using the quadratic approximation method. Hurd and Zhou (2010) introduce a new
formula for spread options pricing based on Fourier analysis of the payoff function. Li,
Zhou, and Deng (2010) provide a closed-form approximation method for pricing spread
options using the extended Kirk’s approximation method (Kirk, 1995). Wu and Chen
(2009, 2011) apply the lognormal approximation technique for pricing the interest rate and

Constant Maturity Swap spread options. Besides, a more detailed and informed survey of
the research on the valuation of European basket and spread options is provided by Lyden
(1996), Carmona and Durrleman (2003), and Lin, Chung, and Yeh (2016).

In recent years, the subprime-loan turmoil and European debt crisis have made
financial markets more volatile and many financial institutions incur credit events,
which makes hedging risks an even more vital issue. Therefore, integrating the pricing
3
and hedging models for various financial derivatives, and developing an efficient and
consistent method for risk management have become important for academic and

practitioner-oriented research. To integrate the pricing formulas of both basket and spread
options, Borovkova, Permana, and van der Weide (2007) adopt the Lognormal-system (LS)
distribution of the Johnson (1949) distribution family to approximate the (real) distribution

of the basket/spread of assets, and then derive a versatile pricing formula which can

3 For example, Chou, Chen, and Yang (2003) study the valuation of covered warrant with credit risk,
Yeh and Yu (2015) employ the SABR-LMM (LIBOR Market Model) model proposed by Mercurio
and Morini (2009) to price interest rate derivatives, and Lin, Chuang, and Fang (2021) explore and
analyze the valuation and risk management of rainfall index. In addition, Lin et al. (2016) review
the existing literature for pricing and hedging derivatives. Lin, Chung, and Yeh (2017) review and
summarize the empirical studies of derivatives markets by conducting a survey with more than 140
papers. All these studies reveal that risk management using derivatives has become an important task
for academic researchers and market-practitioners.

4