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Pricing Product Options and Using Them to Complete Markets for Functions of Two Underlying Asset Prices

Author

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  • Dilip B. Madan

    (Robert H. Smith School of Business, University of Maryland, College Park, MD 20742, USA)

  • King Wang

    (Derivative Product Strats, Morgan Stanley, 1585 Broadway, 5th Floor, New York, NY 10036, USA)

Abstract

Options paying the product of put and/or call option payouts at different strikes on two underlying assets are observed to synthesize joint densities and replicate differentiable functions of two underlying asset prices. The pricing of such options is undertaken from three perspectives. The first perspective uses a geometric two-dimensional Brownian motion model. The second inverts two-dimensional characteristic functions. The third uses a bootstrapped physical measure to propose a risk charge minimizing hedge using options on the two underlying assets. The options are priced at the cost of the hedge plus the risk charge.

Suggested Citation

  • Dilip B. Madan & King Wang, 2021. "Pricing Product Options and Using Them to Complete Markets for Functions of Two Underlying Asset Prices," JRFM, MDPI, vol. 14(8), pages 1-20, August.
    • Handle: RePEc:gam:jjrfmx:v:14:y:2021:i:8:p:355-:d:608072
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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. Dilip B. Madan, 2020. "Multivariate Distributions For Financial Returns," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 23(06), pages 1-32, September.
    3. 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..
    4. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    5. Madan,Dilip & Schoutens,Wim, 2016. "Applied Conic Finance," Cambridge Books, Cambridge University Press, number 9781107151697, October.
    6. Alexander Cherny & Dilip Madan, 2009. "New Measures for Performance Evaluation," The Review of Financial Studies, Society for Financial Studies, vol. 22(7), pages 2371-2406, July.
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    Cited by:

    1. Kopaliani, R. & Denisov, N., 2023. "Composite option pricing and the volatility surface construction," Journal of the New Economic Association, New Economic Association, vol. 60(3), pages 27-48.

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