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Option Pricing in an Investment Risk-Return Setting

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Listed:
  • Abootaleb Shirvani
  • Frank J. Fabozzi
  • Stoyan V. Stoyanov

Abstract

In this paper, we combine modern portfolio theory and option pricing theory so that a trader who takes a position in a European option contract and the underlying assets can construct an optimal portfolio such that at the moment of the contract's maturity the contract is perfectly hedged. We derive both the optimal holdings in the underlying assets for the trader's optimal mean-variance portfolio and the amount of unhedged risk prior to maturity. Solutions assuming the cases where the price dynamics in the underlying assets follow discrete binomial price dynamics, continuous diffusions, stochastic volatility, volatility-of-volatility, and Merton-jump diffusion are derived.

Suggested Citation

  • Abootaleb Shirvani & Frank J. Fabozzi & Stoyan V. Stoyanov, 2020. "Option Pricing in an Investment Risk-Return Setting," Papers 2001.00737, arXiv.org.
    • Handle: RePEc:arx:papers:2001.00737
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    References listed on IDEAS

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    2. Svetlozar T. Rachev & Stoyan V. Stoyanov & Frank J. Fabozzi, 2017. "Financial Markets With No Riskless (Safe) Asset," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 20(08), pages 1-24, December.
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    8. Kim, Y.S. & Stoyanov, S. & Rachev, S. & Fabozzi, F., 2016. "Multi-purpose binomial model: Fitting all moments to the underlying geometric Brownian motion," Economics Letters, Elsevier, vol. 145(C), pages 225-229.
    9. Peter Carr & Anita Mayo, 2007. "On the Numerical Evaluation of Option Prices in Jump Diffusion Processes," The European Journal of Finance, Taylor & Francis Journals, vol. 13(4), pages 353-372.
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    Cited by:

    1. Thilini Mahanama & Abootaleb Shirvani & Svetlozar T. Rachev, 2021. "Global Index on Financial Losses Due to Crime in the United States," JRFM, MDPI, vol. 14(7), pages 1-16, July.
    2. Thilini Mahanama & Abootaleb Shirvani & Svetlozar Rachev, 2022. "A Natural Disasters Index," Environmental Economics and Policy Studies, Springer;Society for Environmental Economics and Policy Studies - SEEPS, vol. 24(2), pages 263-284, April.
    3. Thilini Mahanama & Abootaleb Shirvani & Svetlozar Rachev, 2021. "Global Index on Financial Losses due to Crime in the United States," Papers 2105.03514, arXiv.org.

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