Marking-to-market, stochastic interest rates and discounts on stock index futures

An attempt is made to show that the discounts on stock index futures may occur when interest rates are stochastic and marking-to-market is considered. First, a futures pricing equation is established by discounting the expected cash flows of futures contracts at a required rate of return derived in the framework of the arbitrage pricing theory with inflation risk specified as the 2nd factor. Not only the riskless interest rate but also the volatility of and the correlation between stock returns and interest rates, as well as the pricing of inflation risk, influence the equilibrium price of stock index futures. Based on these results, a justification is provided for the discounts on stock index futures. The model suggests that discounts are likely to occur when interest rates and stock returns are relatively turbulent and negatively related and when a positive inflation risk is priced in the stock index futures. The prevailing method of calculating basis may be inadequate in the search for arbitrage profits.