Non-Tradable S&P 500 Index and the Pricing of Its Traded Derivatives

Abstract

We derive a coherent multi-factor model for pricing various derivatives written on the same underlying (potentially non-tradable) asset. We show the difference between a case in which the underlying asset is self-financed and tradable and a case in which it is not. In the first case, an additional arbitrage condition must be introduced, which implies nontrivial parameter restrictions. These restrictions can be empirically tested to check whether the derivatives are priced as if the underlying were self-financed and tradable. This methodology allows us to define the tradability premium. As an illustration, we compute a daily tradability premium for the S&P 500.The Supplement for this paper is available at the following URL: http://ssrn.com/abstract=2643248