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

58 Pages Posted: 4 Jun 2018

See all articles by Philippe Raimbourg

Philippe Raimbourg

Université Paris I Panthéon-Sorbonne

Paul Zimmermann

Catholic University of Lille - IÉSEG School of Management, Lille Campus

Date Written: June 3, 2018

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.

Keywords: Futures Contracts, Risk Premium, Normal Backwardation, Contango, Stochastic Covariance, Endogenous Covariance

JEL Classification: G13, G12, E43, E52

Suggested Citation

Raimbourg, Philippe and Zimmermann, Paul, Is Normal Backwardation Normal? Valuing Financial Futures with a Stochastic, Endogenous Index-Rate Covariance (June 3, 2018). Paris December 2018 Finance Meeting EUROFIDAI - AFFI. Available at SSRN: https://ssrn.com/abstract=3189847 or http://dx.doi.org/10.2139/ssrn.3189847

Philippe Raimbourg

Université Paris I Panthéon-Sorbonne ( email )

12, place du Panthéon
Paris, IL
France
+33 1 40 46 27 62 (Phone)
+33 1 40 46 31 77 (Fax)

Paul Zimmermann (Contact Author)

Catholic University of Lille - IÉSEG School of Management, Lille Campus ( email )

3 rue de la Digue
Lille, 59000
France

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