IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1106.1395.html
   My bibliography  Save this paper

Utility based pricing and hedging of jump diffusion processes with a view to applications

Author

Listed:
  • Jochen Zahn

Abstract

We discuss utility based pricing and hedging of jump diffusion processes with emphasis on the practical applicability of the framework. We point out two difficulties that seem to limit this applicability, namely drift dependence and essential risk aversion independence. We suggest to solve these by a re-interpretation of the framework. This leads to the notion of an implied drift. We also present a heuristic derivation of the marginal indifference price and the marginal optimal hedge that might be useful in numerical computations.

Suggested Citation

  • Jochen Zahn, 2011. "Utility based pricing and hedging of jump diffusion processes with a view to applications," Papers 1106.1395, arXiv.org, revised Dec 2012.
    • Handle: RePEc:arx:papers:1106.1395
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1106.1395
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Monoyios, Michael, 2004. "Option pricing with transaction costs using a Markov chain approximation," Journal of Economic Dynamics and Control, Elsevier, vol. 28(5), pages 889-913, February.
    2. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    3. A.E. Whalley & P. Wilmott, 1999. "Optimal Hedging of Options with Small but Arbitrary Transaction Cost Structure," OFRC Working Papers Series 1999mf09, Oxford Financial Research Centre.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pelsser, Antoon & Salahnejhad Ghalehjooghi, Ahmad, 2016. "Time-consistent actuarial valuations," Insurance: Mathematics and Economics, Elsevier, vol. 66(C), pages 97-112.
    2. Nicola Cantarutti & Jo~ao Guerra & Manuel Guerra & Maria do Ros'ario Grossinho, 2016. "Option pricing in exponential L\'evy models with transaction costs," Papers 1611.00389, arXiv.org, revised Nov 2019.
    3. Shota Imaki & Kentaro Imajo & Katsuya Ito & Kentaro Minami & Kei Nakagawa, 2021. "No-Transaction Band Network: A Neural Network Architecture for Efficient Deep Hedging," Papers 2103.01775, arXiv.org.
    4. Konstantinos Skindilias & Chia Lo, 2015. "Local volatility calibration during turbulent periods," Review of Quantitative Finance and Accounting, Springer, vol. 44(3), pages 425-444, April.
    5. Carol Alexandra & Leonardo M. Nogueira, 2005. "Optimal Hedging and Scale Inavriance: A Taxonomy of Option Pricing Models," ICMA Centre Discussion Papers in Finance icma-dp2005-10, Henley Business School, University of Reading, revised Nov 2005.
    6. Christophe Chorro & Florian Ielpo & Benoît Sévi, 2017. "The contribution of jumps to forecasting the density of returns," Post-Print halshs-01442618, HAL.
    7. Peter Carr & Liuren Wu, 2014. "Static Hedging of Standard Options," Journal of Financial Econometrics, Oxford University Press, vol. 12(1), pages 3-46.
    8. Kathrin Glau & Ricardo Pachon & Christian Potz, 2019. "Speed-up credit exposure calculations for pricing and risk management," Papers 1912.01280, arXiv.org.
    9. Pringles, Rolando & Olsina, Fernando & Penizzotto, Franco, 2020. "Valuation of defer and relocation options in photovoltaic generation investments by a stochastic simulation-based method," Renewable Energy, Elsevier, vol. 151(C), pages 846-864.
    10. Sandrine Lardic & Claire Gauthier, 2003. "Un modèle multifactoriel des spreads de crédit : estimation sur panels complets et incomplets," Économie et Prévision, Programme National Persée, vol. 159(3), pages 53-69.
    11. René Garcia & Richard Luger & Eric Renault, 2000. "Asymmetric Smiles, Leverage Effects and Structural Parameters," Working Papers 2000-57, Center for Research in Economics and Statistics.
    12. Wang, Jun & Liang, Jin-Rong & Lv, Long-Jin & Qiu, Wei-Yuan & Ren, Fu-Yao, 2012. "Continuous time Black–Scholes equation with transaction costs in subdiffusive fractional Brownian motion regime," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(3), pages 750-759.
    13. Sang Byung Seo & Jessica A. Wachter, 2019. "Option Prices in a Model with Stochastic Disaster Risk," Management Science, INFORMS, vol. 65(8), pages 3449-3469, August.
    14. John Driffill & Turalay Kenc & Martin Sola, 2013. "Real Options With Priced Regime-Switching Risk," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 16(05), pages 1-30.
    15. Hongzhong Zhang, 2018. "Stochastic Drawdowns," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 10078, August.
    16. Carvalho, Augusto & Guimaraes, Bernardo, 2018. "State-controlled companies and political risk: Evidence from the 2014 Brazilian election," Journal of Public Economics, Elsevier, vol. 159(C), pages 66-78.
    17. Jurczenko, Emmanuel & Maillet, Bertrand & Negrea, Bogdan, 2002. "Revisited multi-moment approximate option pricing models: a general comparison (Part 1)," LSE Research Online Documents on Economics 24950, London School of Economics and Political Science, LSE Library.
    18. Viktor Stojkoski & Trifce Sandev & Lasko Basnarkov & Ljupco Kocarev & Ralf Metzler, 2020. "Generalised geometric Brownian motion: Theory and applications to option pricing," Papers 2011.00312, arXiv.org.
    19. Yeap, Claudia & Kwok, Simon S. & Choy, S. T. Boris, 2016. "A Flexible Generalised Hyperbolic Option Pricing Model and its Special Cases," Working Papers 2016-14, University of Sydney, School of Economics.
    20. Chendi Ni & Yuying Li & Peter A. Forsyth, 2023. "Neural Network Approach to Portfolio Optimization with Leverage Constraints:a Case Study on High Inflation Investment," Papers 2304.05297, arXiv.org, revised May 2023.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:1106.1395. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.