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Changes of Numeraire for Pricing Futures, Forwards, and Options

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  • Schroder, Mark

Abstract

A change of numeraire argument is used to derive a general option parity, or equivalence, result relating American call and put prices, and to obtain new expressions for futures and forward prices. The general parity result unifies and extends a number of existing results. The new futures and forward pricing formulas are often simpler to compute in multifactor models than existing alternatives. We also extend previous work by deriving a general formula relating exchange options to ordinary call options. A number of applications to diffusion models, including stochastic volatility, stochastic interest rate, and stochastic dividend rate models, and jump-diffusion models are examined. Article published by Oxford University Press on behalf of the Society for Financial Studies in its journal, The Review of Financial Studies.

Suggested Citation

  • Schroder, Mark, 1999. "Changes of Numeraire for Pricing Futures, Forwards, and Options," Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 1143-1163.
  • Handle: RePEc:oup:rfinst:v:12:y:1999:i:5:p:1143-63
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    2. Fajardo, J. & Mordeckiy, E., 2003. "Pricing Derivatives on Two Lévy-driven Stocks," Finance Lab Working Papers flwp_56, Finance Lab, Insper Instituto de Ensino e Pesquisa.
    3. Jean-Paul Laurent & Philippe Amzelek & Joe Bonnaud, 2014. "An overview of the valuation of collateralized derivative contracts," Review of Derivatives Research, Springer, pages 261-286.
    4. Abraham Lioui, 2005. "Stochastic dividend yields and derivatives pricing in complete markets," Review of Derivatives Research, Springer, pages 151-175.
    5. Fajardo, J. & Mordeckiz, E., 2004. "Duality and Derivative Pricing with Lévy Processes," Finance Lab Working Papers flwp_71, Finance Lab, Insper Instituto de Ensino e Pesquisa.
    6. JosE Fajardo & Ernesto Mordecki, 2006. "Symmetry and duality in Levy markets," Quantitative Finance, Taylor & Francis Journals, pages 219-227.
    7. Medvedev, Alexey & Scaillet, Olivier, 2010. "Pricing American options under stochastic volatility and stochastic interest rates," Journal of Financial Economics, Elsevier, vol. 98(1), pages 145-159, October.
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    11. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
    12. José Fajardo & Ernesto Mordecki, 2005. "Duality and Derivative Pricing with Time-Changed Lévy Processes," IBMEC RJ Economics Discussion Papers 2005-12, Economics Research Group, IBMEC Business School - Rio de Janeiro.
    13. Ruas, João Pedro & Dias, José Carlos & Vidal Nunes, João Pedro, 2013. "Pricing and static hedging of American-style options under the jump to default extended CEV model," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4059-4072.
    14. Anna Battauz & Marzia De Donno & Alessandro Sbuelz, 2015. "Real Options and American Derivatives: The Double Continuation Region," Management Science, INFORMS, pages 1094-1107.
    15. Cai, Ning & Sun, Lihua, 2014. "Valuation of stock loans with jump risk," Journal of Economic Dynamics and Control, Elsevier, vol. 40(C), pages 213-241.
    16. Marzia De Donno & Zbigniew Palmowski & Joanna Tumilewicz, 2017. "Double continuation regions for American and Swing options with negative discount rate in L\'evy models," Papers 1801.00266, arXiv.org.
    17. José Carlos Dias & João Pedro Vidal Nunes & João Pedro Ruas, 2015. "Pricing and static hedging of European-style double barrier options under the jump to default extended CEV model," Quantitative Finance, Taylor & Francis Journals, pages 1995-2010.
    18. Anna Battauz & Marzia De Donno & Alessandro Sbuelz, 2015. "Real Options and American Derivatives: The Double Continuation Region," Management Science, INFORMS, pages 1094-1107.
    19. Jérôme Detemple & Weidong Tian, 2002. "The Valuation of American Options for a Class of Diffusion Processes," Management Science, INFORMS, pages 917-937.
    20. S. G. Kou & Hui Wang, 2004. "Option Pricing Under a Double Exponential Jump Diffusion Model," Management Science, INFORMS, pages 1178-1192.
    21. Leippold, Markus & Vasiljević, Nikola, 2017. "Pricing and disentanglement of American puts in the hyper-exponential jump-diffusion model," Journal of Banking & Finance, Elsevier, vol. 77(C), pages 78-94.
    22. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    23. Lin, Yueh-Neng, 2013. "VIX option pricing and CBOE VIX Term Structure: A new methodology for volatility derivatives valuation," Journal of Banking & Finance, Elsevier, vol. 37(11), pages 4432-4446.

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