On the Use of Numeraires in Option pricing
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.
|Date of creation:||03 Jan 2002|
|Date of revision:|
|Publication status:||Published in Journal of Derivatives, 2002, pages 43-58.|
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- 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.
- 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.
- 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.
- 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.
- Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 205-09, March.
- Huddart, Steven, 1994. "Employee stock options," Journal of Accounting and Economics, Elsevier, vol. 18(2), pages 207-231, September.
- 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.
- 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.
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