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On the Use of Numeraires in Option pricing

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Author Info

  • Benninga, Simon

    ()
    (Faculty of Management, Tel Aviv University)

  • Björk, Tomas

    ()
    (Dept. of Finance, Stockholm School of Economics)

  • Wiener, Zvi

    ()
    (School of Business, Hebrew University of Jerusalem)

Abstract

In this paper we discuss the significant computational simplification that occurs when option pricing is approached through the change of numeraire technique. The original impetus was a recently published paper (Hoang, Powell, Shi 1999) on endowment options; in the present paper we extend these results to the case of stochastic interest rates. We also discuss four additional option pricing problems within the framework of a change of numeraire: 1. Pricing savings plans which incorporate a choice of linkage. 2. Pricing convertible bonds. 3. Pricing employee stock ownership plans 4. Pricing options where the strike price is in a currency different from the stock price.

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Bibliographic Info

Paper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 484.

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Length: 25 pages
Date of creation: 03 Jan 2002
Date of revision:
Publication status: Published in Journal of Derivatives, 2002, pages 43-58.
Handle: RePEc:hhs:hastef:0484

Note: submitted
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Postal: The Economic Research Institute, Stockholm School of Economics, P.O. Box 6501, 113 83 Stockholm, Sweden
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Related research

Keywords: Numeraire; option; convertible bond;

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References

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  1. Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 205-09, March.
  2. Chip Heath & Steven Huddart & Mark Lang, 1999. "Psychological Factors And Stock Option Exercise," The Quarterly Journal of Economics, MIT Press, vol. 114(2), pages 601-627, May.
  3. Brennan, M J & Schwartz, Eduardo S, 1977. "Convertible Bonds: Valuation and Optimal Strategies for Call and Conversion," Journal of Finance, American Finance Association, vol. 32(5), pages 1699-1715, December.
  4. Huddart, Steven, 1994. "Employee stock options," Journal of Accounting and Economics, Elsevier, vol. 18(2), pages 207-231, September.
  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. Brenner, Menachem & Galai, Dan, 1978. "The determinants of the return on index bonds," Journal of Banking & Finance, Elsevier, vol. 2(1), pages 47-64, June.
  7. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-86, March.
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Citations

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Cited by:
  1. Nikolai Dokuchaev, 2011. "On martingale measures and pricing for continuous bond-stock market with stochastic bond," Papers 1108.0719, arXiv.org, revised May 2013.
  2. Massoud Heidari & Liuren WU, 2002. "Are Interest Rate Derivatives Spanned by the Term Structure of Interest Rates?," Finance 0207013, EconWPA.
  3. Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
  4. Yoram Landskroner & Alon Raviv, 2004. "The Valuation of Inflation-Indexed and FX Convertible Bonds," Finance 0401005, EconWPA.
  5. Carr, Peter & Wu, Liuren, 2004. "Time-changed Levy processes and option pricing," Journal of Financial Economics, Elsevier, vol. 71(1), pages 113-141, January.
  6. Hyong-chol O & Yong-hwa Ro & Ning Wan, 2013. "The Use of Numeraires in Multi-dimensional Black-Scholes Partial Differential Equations," Papers 1310.8296, arXiv.org, revised Nov 2013.

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