Review of Quantitative Finance and Accounting, 23: 167–184, 2004
2004 Kluwer Academic Publishers. Manufactured in The Netherlands.
Price Expectation and the Pricing of Stock Index Futures
Professor, Department of Finance, Southern Taiwan University of Technology, Tainan, Taiwan, Republic of China
Associate Professor, Department of Financial Operations, National Kaohsiung First University of Science and
Technology, Kaohsiung, Taiwan, Republic of China
Abstract. Capital markets are not perfect or frictionless, and arbitrage mechanism cannot be complete, par-
ticularly for index arbitrage. This study constructs a theoretical foundation to explain why the price expectation
of the underlying asset should be entered into the pricing formula of stock index futures. The price expectation
and incompleteness of arbitrage then are taken into account to develop a pricing model of stock index futures
in imperfect markets. This study also presents three approaches for estimating the model parameter. Finally, the
concept of the degree of market imperfection is deﬁned and the valuation model is provided.
Keywords: price expectation, market imperfection, degree of market imperfection, implied method
JEL Classiﬁcation: G13, C00
Pricing is a key issue for traders of stock index futures and academic researchers. Until
now, the cost of carry model has been the most widely used model for pricing stock index
futures. This model was developed under the assumption of perfect markets and no-arbitrage
arguments. However, market conditions in the real world frequently violate the assumption
of perfect markets. Consequently, several researchers have found a signiﬁcant discrepancy
between actual futures prices and theoretical values estimated by the cost of carry model.
Forexample, Cornell and French (1983a, 1983b), Figlewski (1984), Modest and Sundaresan
(1983), Eytan and Harpaz (1986), and Gay and Jung (1999) all observe that actual futures
prices are below the corresponding values predicted by the cost of carry model.
In fact, capital markets are not perfect or frictionless. First, index arbitrage involves trans-
action costs, including commissions, bid-ask spread, and taxes. As for hedged portfolios,
transaction costs increase limitlessly as the adjustment period approaches zero. Figlewski
(1989) ﬁnds that rebalancing the hedged portfolio daily until option expiration would be
exposed to large risk and transaction costs in real markets. Second, there are restrictions
on short sales and securities are not perfectly divisible. Under the uptick rule, a stock is
required to uptick before selling short. Gay and Jung (1999) argue that transaction costs