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

19 Pages Posted: 27 Apr 2021 Last revised: 17 Sep 2021

See all articles by Stephan Höcht

Stephan Höcht

Technische Universität München (TUM)

Dilip B. Madan

University of Maryland - Robert H. Smith School of Business

Wim Schoutens

KU Leuven - Department of Mathematics

Eva Verschueren

KU Leuven - Department of Accounting, Finance and Insurance

Date Written: August 20, 2020

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 a variety of option surfaces of stock indices, assessing the stability over time of the zero-risk premium strike of a European call option.

Keywords: Pricing density, Physical density, Stock models, Bilateral Gamma, Tilted Bilateral Gamma, Calibration, Risk premium, Call options, S\&P500, DAX

JEL Classification: C00, G00

Suggested Citation

Höcht, Stephan and Madan, Dilip B. and Schoutens, Wim and Verschueren, Eva, It Takes Two to Tango: Estimation of the Zero-Risk Premium Strike of a Call Option Via Joint Physical and Pricing Density Modeling (August 20, 2020). Available at SSRN: https://ssrn.com/abstract=3827031 or http://dx.doi.org/10.2139/ssrn.3827031

Stephan Höcht

Technische Universität München (TUM) ( email )

Arcisstrasse 21
Munich, DE 80333
Germany

Dilip B. Madan

University of Maryland - Robert H. Smith School of Business ( email )

College Park, MD 20742-1815
United States
301-405-2127 (Phone)
301-314-9157 (Fax)

Wim Schoutens

KU Leuven - Department of Mathematics ( email )

Celestijnenlaan 200 B
Leuven, B-3001
Belgium

Eva Verschueren (Contact Author)

KU Leuven - Department of Accounting, Finance and Insurance ( email )

Naamsestraat 69
Leuven, B-3000
Belgium

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