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Incompleteness of markets driven by a mixed diffusion

Author

Listed:
  • N. Bellamy

    (Equipe d'analyse et probabilitÊs, UniversitÊ d'Evry Val d'Essonne, Boulevard des coquibus, F-91025 Evry Cedex, France Manuscript)

  • M. Jeanblanc

    (Equipe d'analyse et probabilitÊs, UniversitÊ d'Evry Val d'Essonne, Boulevard des coquibus, F-91025 Evry Cedex, France Manuscript)

Abstract

An incomplete market driven by a pair of Wiener and Poisson processes is considered. The range of European and American claim prices is determined.

Suggested Citation

  • N. Bellamy & M. Jeanblanc, 2000. "Incompleteness of markets driven by a mixed diffusion," Finance and Stochastics, Springer, vol. 4(2), pages 209-222.
    • Handle: RePEc:spr:finsto:v:4:y:2000:i:2:p:209-222
    Note: received: July 1997; final version received: April 1999
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    Citations

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    Cited by:

    1. Erik Ekstrom & Johan Tysk, 2006. "Convexity preserving jump-diffusion models for option pricing," Papers math/0601526, arXiv.org.
    2. Jean-Luc Prigent, 2001. "Option Pricing with a General Marked Point Process," Mathematics of Operations Research, INFORMS, vol. 26(1), pages 50-66, February.
    3. Bellamy, Nadine, 2001. "Wealth optimization in an incomplete market driven by a jump-diffusion process," Journal of Mathematical Economics, Elsevier, vol. 35(2), pages 259-287, April.
    4. Leonel Perez-hernandez, 2007. "On the existence of an efficient hedge for an American contingent claim within a discrete time market," Quantitative Finance, Taylor & Francis Journals, vol. 7(5), pages 547-551.
    5. Ole Barndorff-Nielsen & Elisa Nicolato & Neil Shephard, 2002. "Some recent developments in stochastic volatility modelling," Quantitative Finance, Taylor & Francis Journals, vol. 2(1), pages 11-23.
    6. Branger, Nicole & Mahayni, Antje, 2006. "Tractable hedging: An implementation of robust hedging strategies," Journal of Economic Dynamics and Control, Elsevier, vol. 30(11), pages 1937-1962, November.
    7. Karl Friedrich Mina & Gerald H. L. Cheang & Carl Chiarella, 2015. "Approximate Hedging Of Options Under Jump-Diffusion Processes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 18(04), pages 1-26.
    8. Mingxin Xu, 2006. "Risk measure pricing and hedging in incomplete markets," Annals of Finance, Springer, vol. 2(1), pages 51-71, January.
    9. Erik Ekstrom & Johan Tysk, 2005. "Properties of option prices in models with jumps," Papers math/0509232, arXiv.org, revised Nov 2005.
    10. George M. Mukupa & Elias R. Offen, 2020. "The Semimartingale Equilibrium Risk Premium for a Risk Seeking Investor," Journal of Mathematics Research, Canadian Center of Science and Education, vol. 12(4), pages 1-13, August.
    11. Leonel Pérez-Hernández, 2005. "On the Existence of Efficient Hedge for an American Contingent Claim: Discrete Time Market," Department of Economics and Finance Working Papers EC200505, Universidad de Guanajuato, Department of Economics and Finance.
    12. 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.
    13. Erik Ekstrom & Johan Tysk, 2007. "Convexity theory for the term structure equation," Papers math/0702435, arXiv.org.
    14. Bergenthum Jan & Rüschendorf Ludger, 2008. "Comparison results for path-dependent options," Statistics & Risk Modeling, De Gruyter, vol. 26(1), pages 53-72, March.
    15. Nikita Ratanov, 2016. "Option Pricing Under Jump-Diffusion Processes with Regime Switching," Methodology and Computing in Applied Probability, Springer, vol. 18(3), pages 829-845, September.
    16. Luciano Campi & Simon Polbennikov & Sbuelz, 2005. "Assessing Credit with Equity: A CEV Model with Jump to Default," Working Papers 24/2005, University of Verona, Department of Economics.
    17. Xavier De Scheemaekere, 2009. "Upper and lower bounds on dynamic risk indifference prices in incomplete markets," Papers 0909.3219, arXiv.org, revised Sep 2010.
    18. Jan Bergenthum & Ludger Rüschendorf, 2006. "Comparison of Option Prices in Semimartingale Models," Finance and Stochastics, Springer, vol. 10(2), pages 222-249, April.
    19. Laura Pasin & Tiziano Vargiolu, 2010. "Optimal Portfolio for CRRA Utility Functions when Risky Assets are Exponential Additive Processes," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 39(1‐2), pages 65-90, February.
    20. Breton, Jean-Christophe & Privault, Nicolas, 2024. "Wasserstein distance estimates for jump-diffusion processes," Stochastic Processes and their Applications, Elsevier, vol. 172(C).
    21. Campi, Luciano & Polbennikov, Simon & Sbuelz, Alessandro, 2009. "Systematic equity-based credit risk: A CEV model with jump to default," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 93-108, January.

    More about this item

    Keywords

    Contingent claim valuation; incomplete model; martingale measures; Black and Scholes function;
    All these keywords.

    JEL classification:

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

    Statistics

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