It Takes Two to Tango: Estimation of the Zero-Risk Premium Strike of a Call Option via Joint Physical and Pricing Density Modeling

Stephan Höcht, Dilip B. Madan, Wim Schoutens and Eva Verschueren
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Stephan Höcht: Assenagon GmbH, Prannerstraße 8, 80333 München, Germany
Dilip B. Madan: Robert H. Smith School of Business, University of Maryland, College Park, MD 20742, USA
Wim Schoutens: Department of Mathematics, University of Leuven, Celestijnenlaan 200B, 3001 Leuven, Belgium
Eva Verschueren: Department of Accounting, Finance and Insurance, University of Leuven, Naamsestraat 69, 3000 Leuven, Belgium

Risks, 2021, vol. 9, issue 11, 1-19

Abstract: It is generally said that out-of-the-money call options are expensive and one can ask the question from which moneyness level this is the case. Expensive actually means that the price one pays for the option is more than the discounted average payoff one receives. If so, the option bears a negative risk premium. The objective of this paper is to investigate the zero-risk premium moneyness level of a European call option, i.e., the strike where expectations on the option’s payoff in both the P - and Q -world are equal. To fully exploit the insights of the option market we deploy the Tilted Bilateral Gamma pricing model to jointly estimate the physical and pricing measure from option prices. We illustrate the proposed pricing strategy on the option surface of stock indices, assessing the stability and position of the zero-risk premium strike of a European call option. With small fluctuations around a slightly in-the-money level, on average, the zero-risk premium strike appears to follow a rather stable pattern over time.

Keywords: pricing density; physical density; bilateral gamma; tilted bilateral gamma; call option; risk premium (search for similar items in EconPapers)
JEL-codes: C G0 G1 G2 G3 K2 M2 M4 (search for similar items in EconPapers)
Date: 2021
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