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On the Use of Numeraires in Option pricing

  • 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)

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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Paper provided by Stockholm School of Economics in its series SSE/EFI 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
Contact details of provider: Postal: The Economic Research Institute, Stockholm School of Economics, P.O. Box 6501, 113 83 Stockholm, Sweden
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  1. 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.
  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. 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.
  4. Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 205-09, March.
  5. 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.
  6. 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.
  7. Fischer, Stanley, 1978. "Call Option Pricing when the Exercise Price Is Uncertain, and the Valuation of Index Bonds," Journal of Finance, American Finance Association, vol. 33(1), pages 169-76, March.
  8. Huddart, Steven, 1994. "Employee stock options," Journal of Accounting and Economics, Elsevier, vol. 18(2), pages 207-231, September.
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