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Numeraire Invariance and application to Option Pricing and Hedging

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  • Jamshidian, Farshid
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    Abstract

    This is a short version of the paper of Exchange Options (2007), concentrating on the principle of numeraire invariance. It emphasizes application to unique pricing in arbitrage-free model, the derivation of hedge ratios and the PDE when price ratios are diffusions, explicit representations in the multivariate Poisson model, and the role played by homogeneity.

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    File URL: http://mpra.ub.uni-muenchen.de/7167/
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    Bibliographic Info

    Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 7167.

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    Date of creation: 14 Feb 2008
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    Handle: RePEc:pra:mprapa:7167

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    Keywords: Numeraire invariance; hedging; self-financing trading strategy; predictable representation; unique pricing; arbitrage-free; martingale; homogeneous payoff; Markovian; It\^o's formula; SDE; PDE; geometric Brownian motion; exponential Poisson process;

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    References

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    1. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    2. 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.
    3. Farshid Jamshidian, 1993. "Option and Futures Evaluation With Deterministic Volatilities," Mathematical Finance, Wiley Blackwell, vol. 3(2), pages 149-159.
    4. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
    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. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
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    Cited by:
    1. Nicolas Privault & Timothy Robin Teng, 2013. "Hedging in bond markets by the Clark-Ocone formula," Papers 1304.6165, arXiv.org.

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