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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
    1. Dilip B. Madan & Peter P. Carr & Eric C. Chang, 1998. "The Variance Gamma Process and Option Pricing," Review of Finance, European Finance Association, vol. 2(1), pages 79-105.
    2. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    3. Alejandro Bernales & Gonzalo Cortazar & Luka Salamunic & George Skiadopoulos, 2020. "Learning and Index Option Returns," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 38(2), pages 327-339, April.
    4. Joshua D. Coval & Tyler Shumway, 2001. "Expected Option Returns," Journal of Finance, American Finance Association, vol. 56(3), pages 983-1009, June.
    5. Harrison, J. Michael & Pliska, Stanley R., 1981. "Martingales and stochastic integrals in the theory of continuous trading," Stochastic Processes and their Applications, Elsevier, vol. 11(3), pages 215-260, August.
    6. Madan,Dilip & Schoutens,Wim, 2016. "Applied Conic Finance," Cambridge Books, Cambridge University Press, number 9781107151697.
    7. Dilip B. Madan & Wim Schoutens & King Wang, 2020. "Bilateral multiple gamma returns: Their risks and rewards," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 7(01), pages 1-27, March.
    8. Stoll, Hans R, 1969. "The Relationship between Put and Call Option Prices," Journal of Finance, American Finance Association, vol. 24(5), pages 801-824, December.
    9. Bakshi, Gurdip & Madan, Dilip & Panayotov, George, 2010. "Returns of claims on the upside and the viability of U-shaped pricing kernels," Journal of Financial Economics, Elsevier, vol. 97(1), pages 130-154, July.
    10. Mark Broadie & Mikhail Chernov & Michael Johannes, 2009. "Understanding Index Option Returns," The Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4493-4529, November.
    11. Oleg Bondarenko, 2014. "Why Are Put Options So Expensive?," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 4(03), pages 1-50.
    12. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    13. Chaudhury, Mo, 2017. "Volatility and expected option returns: A note," Economics Letters, Elsevier, vol. 152(C), pages 1-4.
    14. David Volkmann, 2021. "Explaining S&P500 option returns: an implied risk-adjusted approach," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 29(2), pages 665-685, June.
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