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Numeraire Invariance and application to Option Pricing and Hedging

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  • Jamshidian, Farshid

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.

Suggested Citation

  • Jamshidian, Farshid, 2008. "Numeraire Invariance and application to Option Pricing and Hedging," MPRA Paper 7167, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:7167
    as

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    File URL: https://mpra.ub.uni-muenchen.de/7167/1/MPRA_paper_7167.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. Farshid Jamshidian, 1993. "Option and Futures Evaluation With Deterministic Volatilities1," Mathematical Finance, Wiley Blackwell, vol. 3(2), pages 149-159, April.
    3. 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.
    4. Robert C. Merton, 2005. "Theory of rational option pricing," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 8, pages 229-288, World Scientific Publishing Co. Pte. Ltd..
    5. 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 637-654, May-June.
    6. Margrabe, William, 1978. "The Value of an Option to Exchange One Asset for Another," Journal of Finance, American Finance Association, vol. 33(1), pages 177-186, March.
    Full references (including those not matched with items on IDEAS)

    Citations

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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.
    2. Nikolai Dokuchaev, 2018. "On the implied market price of risk under the stochastic numéraire," Annals of Finance, Springer, vol. 14(2), pages 223-251, May.

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    More about this item

    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;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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