Returns of Claims on the Upside and the Viability of U-Shaped Pricing Kernels
56 Pages Posted: 28 Aug 2009 Last revised: 30 Sep 2018
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Returns of Claims on the Upside and the Viability of U-Shaped Pricing Kernels
Returns of Claims on the Upside and the Viability of U-Shaped Pricing Kernels
Date Written: July 31, 2009
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.
Keywords: U-shaped pricing kernels, claims on the upside, negative call returns, short-selling, heterogeneity in beliefs
JEL Classification: G0, G10, G11, G12, G13, C5, D24
Suggested Citation: Suggested Citation
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