Returns of Claims on the Upside and the Viability of U-Shaped Pricing Kernels

Abstract:     
When the pricing kernel is U-shaped, then expected returns of claims with payout on the upside are negative for strikes beyond a threshold, determined by the slope of the U-shaped kernel in its increasing region, and have negative partial derivative with respect to strike in the increasing region of the kernel. Using returns of (i) S&P 500 index calls, (ii) calls on major international equity indexes, (iii) digital calls, (iv) upside variance contracts, and (v) a theoretical construct that we denote as kernel call, we find broad support for the implications of U-shaped pricing kernels. A possible theoretical reconciliation of our empirical findings is explored through a model that accommodates heterogeneity in beliefs about return outcomes and short-selling.

Number of Pages in PDF File: 55

Keywords: U-shaped pricing kernels, claims on the upside, monotonically declining pricing kernels,

JEL Classification: G, G1, G11, G12, G13, C5, D24

Accepted Paper Series