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On the implied market price of risk under the stochastic numéraire

Author

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  • Nikolai Dokuchaev

    (Curtin University
    National Research University ITMO)

Abstract

This papers addresses the stock option pricing problem in a continuous time market model where there are two stochastic tradable assets, and one of them is selected as a numéraire. An equivalent martingale measure is not unique for this market, and there are non-replicable claims. Some rational choices of the equivalent martingale measures are suggested and discussed, including implied measures calculated from bond prices constructed as a risk-free investment with deterministic payoff at the terminal time. This leads to possibility to infer a implied market price of risk process from observed historical bond prices.

Suggested Citation

  • 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.
    • Handle: RePEc:kap:annfin:v:14:y:2018:i:2:d:10.1007_s10436-017-0315-y
    DOI: 10.1007/s10436-017-0315-y
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    References listed on IDEAS

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    1. Ioannis Karatzas & Constantinos Kardaras, 2007. "The numéraire portfolio in semimartingale financial models," Finance and Stochastics, Springer, vol. 11(4), pages 447-493, October.
    2. Kardaras, Constantinos, 2010. "Numéraire-invariant preferences in financial modeling," LSE Research Online Documents on Economics 44993, London School of Economics and Political Science, LSE Library.
    3. Schroder, Mark, 1999. "Changes of Numeraire for Pricing Futures, Forwards, and Options," The Review of Financial Studies, Society for Financial Studies, vol. 12(5), pages 1143-1163.
    4. Johannes Ruf, 2012. "Negative Call Prices," Papers 1204.1903, arXiv.org, revised Jan 2013.
    5. M. J. Brennan, 1998. "The Role of Learning in Dynamic Portfolio Decisions," Review of Finance, European Finance Association, vol. 1(3), pages 295-306.
    6. Jan Vecer & Mingxin Xu, 2004. "Pricing Asian options in a semimartingale model," Quantitative Finance, Taylor & Francis Journals, vol. 4(2), pages 170-175.
    7. Nikolai Dokuchaev, 2011. "Option Pricing Via Maximization Over Uncertainty And Correction Of Volatility Smile," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 14(04), pages 507-524.
    8. Jamshidian, Farshid, 2008. "Numeraire Invariance and application to Option Pricing and Hedging," MPRA Paper 7167, University Library of Munich, Germany.
    9. Cheng, Susan T., 1991. "On the feasibility of arbitrage-based option pricing when stochastic bond price processes are involved," Journal of Economic Theory, Elsevier, vol. 53(1), pages 185-198, February.
    10. Calum G. Turvey & Sridar Komar, 2007. "Martingale Restrictions and the Implied Market Price of Risk," Canadian Journal of Agricultural Economics/Revue canadienne d'agroeconomie, Canadian Agricultural Economics Society/Societe canadienne d'agroeconomie, vol. 55(1), pages 138-158, March.
    11. Lin-Yee Hin & Nikolai Dokuchaev, 2014. "On the implied volatility layers under the future risk-free rate uncertainty," International Journal of Financial Markets and Derivatives, Inderscience Enterprises Ltd, vol. 3(4), pages 392-408.
    12. Johannes Ruf, 2013. "Negative call prices," Annals of Finance, Springer, vol. 9(4), pages 787-794, November.
    13. Weron, Rafal, 2008. "Market price of risk implied by Asian-style electricity options and futures," Energy Economics, Elsevier, vol. 30(3), pages 1098-1115, May.
    14. 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.
    15. Aziz Issaka & Indranil SenGupta, 2017. "Analysis of variance based instruments for Ornstein–Uhlenbeck type models: swap and price index," Annals of Finance, Springer, vol. 13(4), pages 401-434, November.
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    Cited by:

    1. Nikolai Dokuchaev, 2019. "A gap between rational annuitization price for producer and price for customer," Journal of Revenue and Pricing Management, Palgrave Macmillan, vol. 18(2), pages 147-154, April.
    2. Nikolai Dokuchaev, 2018. "On a gap between rational annuitization price for producer and price for customer," Papers 1809.08960, arXiv.org.

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    More about this item

    Keywords

    Implied parameters; Market price of risk; Random numéraire; Stochastic bond price; Incomplete market;
    All these keywords.

    JEL classification:

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

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