Is Normal Backwardation Normal? Valuing Financial Futures with a Stochastic, Endogenous Index-Rate Covariance

Abstract

Revisiting the two-factor valuation of financial futures contracts and their derivatives, we propose a new approach in which the covariance process between the underlying asset price and the money market interest rate is set endogenously according to investors' arbitrage operations. The asset-rate covariance turns out to be stochastic, thereby explicitly capturing futures contracts' marking-to-market feature. Our numerical simulations show significant deviations from the traditional cost-of-carry model of futures prices, in line with Cox, Ingersoll and Ross's (1981) theory and a large corpus of past empirical research. Our empirical tests show an impact of several index points magnitude from the recent US Federal Reserve interest rate hikes on the S&P 500 daily spot-futures basis, highlighting the effect of monetary policy at low frequencies on the backwardation vs. contango regime, and shedding new light on Keynes's (1930) theory of normal backwardation.