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The Use of Numeraires in Multi-dimensional Black-Scholes Partial Differential Equations

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  • Hyong-chol O
  • Yong-hwa Ro
  • Ning Wan

Abstract

The change of numeraire gives very important computational simplification in option pricing. This technique reduces the number of sources of risks that need to be accounted for and so it is useful in pricing complicated derivatives that have several sources of risks. In this article, we considered the underlying mathematical theory of numeraire technique in the viewpoint of PED theory and illustrated it with five concrete pricing problems. In the viewpoint of PED theory, the numeraire technique is a method of reducing the dimension of status spaces where PDE is defined.

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  • 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 Jul 2014.
    • Handle: RePEc:arx:papers:1310.8296
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    3. Benninga, Simon & Björk, Tomas & Wiener, Zvi, 2002. "On the Use of Numeraires in Option pricing," SSE/EFI Working Paper Series in Economics and Finance 484, Stockholm School of Economics.
    4. Garman, Mark B. & Kohlhagen, Steven W., 1983. "Foreign currency option values," Journal of International Money and Finance, Elsevier, vol. 2(3), pages 231-237, December.
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