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Pricing and hedging basket options to prespecified levels of acceptability

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  • Dilip Madan

Abstract

The concept of stress levels embedded in S&P500 options is defined and illustrated with explicit constructions. The particular example of a stress function used is MINMAXVAR. Seven joint laws for the top 50 stocks in the index are considered. The first time changes a Gaussian one factor copula. The remaining six employ correlated Brownian motion independently time changed in each coordinate. Four models use daily returns, either run as Levy processes or scaled to the option maturity. The last two employ risk-neutral marginals from the VGSSD and CGMYSSD Sato processes. The smallest stress function uses CGMYSSD risk-neutral marginals and Levy correlation. Running the Levy process yields a lower stress surface than scaling to the option maturity. Static hedging of basket options to a particular level of acceptability is shown to substantially lower the price at which the basket option may be offered.

Suggested Citation

  • Dilip Madan, 2010. "Pricing and hedging basket options to prespecified levels of acceptability," Quantitative Finance, Taylor & Francis Journals, vol. 10(6), pages 607-615.
    • Handle: RePEc:taf:quantf:v:10:y:2010:i:6:p:607-615
    DOI: 10.1080/14697680902878113
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    References listed on IDEAS

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    Cited by:

    1. Rand Kwong Yew Low, 2018. "Vine copulas: modelling systemic risk and enhancing higher‐moment portfolio optimisation," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 58(S1), pages 423-463, November.
    2. Cerrato, Mario & Crosby, John & Kaleem, Muhammad, 2011. "Measuring the Economic Significance of Structural Exchange Rate Models," SIRE Discussion Papers 2011-62, Scottish Institute for Research in Economics (SIRE).
    3. Dilip B. Madan & Martijn Pistorius & Wim Schoutens, 2013. "The valuation of structured products using Markov chain models," Quantitative Finance, Taylor & Francis Journals, vol. 13(1), pages 125-136, January.
    4. Dilip Madan, 2011. "Joint risk-neutral laws and hedging," IISE Transactions, Taylor & Francis Journals, vol. 43(12), pages 840-850.
    5. Ping Wu & Robert J. Elliott, 2017. "A simple efficient approximation to price basket stock options with volatility smile," Annals of Finance, Springer, vol. 13(1), pages 1-29, February.
    6. Yu, Bo & Zhu, Hongmei & Wu, Ping, 2022. "The closed-form approximation to price basket options under stochastic interest rate," Finance Research Letters, Elsevier, vol. 46(PB).

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