Examination of the Cost-of-Carry Formula for Futures Contracts on WIG20. Wavelet and Nonlinear Cointegration Analysis

Abstract

The instantaneous and non-instantaneous dependences between spot and futures index prices has been subject of numerous empirical investigations. The theoretical background of these studies is the cost-ofcarry model introduced by [15]. The cost-of-carry model is an arbitrage relationship based on comparison between two alternative methods of acquiring an asset at some future date. In the first method an asset is purchased now and held until this future date. In the second case a futures contract with maturity on the required date is bought. The present value of the futures contract is invested at the risk free interest rate until delivery of the underlying asset at the maturity date. Arbitrage should ensure that the difference between the current asset price and the futures contract price is the cost of carrying the asset, which involves dividend yields and interest rates. The cost-of-carry formula gives the fair price of the futures contract: $$ F_{t,T} = S_t e^{\left( {r_t - d_t } \right)\left( {T - t} \right)} $$ (1) where St is the security index price at time t, F t,T is the index futures price at time t with maturity T, r t is the risk free interest rate, d t is the dividend yield on the security index, and (T — t) is the time to maturity of the futures contract. Taking logarithms of both sides of equation (1) we get: $$ f_{t,T} = s_t + \left( {r_t - d_t } \right)\left( {T - t} \right) $$ (2)