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

Author

Listed:
  • 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)

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.

Suggested Citation

  • Stephan Höcht & Dilip B. Madan & Wim Schoutens & Eva Verschueren, 2021. "It Takes Two to Tango: Estimation of the Zero-Risk Premium Strike of a Call Option via Joint Physical and Pricing Density Modeling," Risks, MDPI, vol. 9(11), pages 1-19, November.
    • Handle: RePEc:gam:jrisks:v:9:y:2021:i:11:p:196-:d:671908
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    References listed on IDEAS

    as
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