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Valuation of Spread and Basket Options

1. Introduction

A spread option is a financial contract on the price difference between several assets.
The underlying assets may include stocks, stock indexes, interest rates, foreign exchange

rates, or commodities. A variety of spread options are widely traded both on exchanges
and in over-the-counter markets. Investors may use them to speculate or hedge the spread
(correlation) risk. For example, in the agriculture market, soybean crush options traded on
the Chicago Board of Trade are written on the price difference between raw soybean and

two soybean products — namely soybean oil and soybean meal. They can be used to lock
in the producer's profit.
In the energy market, crack spread options written on the price spread between
crude oil and several refined products are traded on the New York Mercantile Exchange.

Electricity spark spread options traded in the over-the-counter market can be used to hedge
the profit of producing electricity with natural gas. As for hedging interest-rate risks,
interest-rate spread options, such as Constant Maturity Swap rate (CMS) spread options,
can be used to hedge the spread between long- and short-term interest rates. Credit spread

options can be traded on the credit spread between two counterparties with different credit-
quality levels. 1
After the collapse of the Bretton-Woods exchange rate system, the exchange rates
between major currencies have become significantly volatile. Thus, managing currency

risk becomes a vital issue, especially for multinational corporations involved in exporting
2
and/or importing goods. For example, a globally-diversified corporation may generate
receivables in some currencies by exporting products and payables in other currencies by
importing materials or equipment. To manage the multi-currency exchange rate risks of

assets (receivables) and liabilities (payables), treasurers may use currency spread options
to neutralize currency risks.

1 For more information about the credit risk, the interest rate risk, and its related empirical studies,
refer to Augustin, Sokolovski, Subrahmanyam, and Tomio (2022), Christensen, Kjær, and Veliyev
(2023), Hasan, Marra, To, Wu, and Zhang (2023), Jaskowski and Rettl (2023), and Telg, Dubinova,
and Lucas (2023).
2 Flood and Rose (1999) and Frömmel and Menkhoff (2003) indicate that the major floating exchange
rates have become more and more volatile since 1973.

2