IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2412.04589.html

Inverting the Markovian projection for pure jump processes

Author

Listed:
  • Martin Larsson
  • Shukun Long

Abstract

Markovian projections arise in problems where we aim to mimic the one-dimensional marginal laws of an It\^o semimartingale by using another It\^o process with Markovian dynamics. In applications, Markovian projections are useful in calibrating jump-diffusion models with both local and stochastic features, leading to the study of the inversion problems. In this paper, we invert the Markovian projections for pure jump processes, which can be used to construct calibrated local stochastic intensity (LSI) models for credit risk applications. Such models are jump process analogues of the notoriously hard to construct local stochastic volatility (LSV) models used in equity modeling.

Suggested Citation

  • Martin Larsson & Shukun Long, 2024. "Inverting the Markovian projection for pure jump processes," Papers 2412.04589, arXiv.org, revised Nov 2025.
    • Handle: RePEc:arx:papers:2412.04589
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2412.04589
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. R. J. Elliott & M. Jeanblanc & M. Yor, 2000. "On Models of Default Risk," Mathematical Finance, Wiley Blackwell, vol. 10(2), pages 179-195, April.
    2. Aurélien Alfonsi & Céline Labart & Jérôme Lelong, 2016. "Stochastic Local Intensity Loss Models With Interacting Particle Systems," Mathematical Finance, Wiley Blackwell, vol. 26(2), pages 366-394, April.
    3. Benjamin Jourdain & Alexandre Zhou, 2020. "Existence of a calibrated regime switching local volatility model," Mathematical Finance, Wiley Blackwell, vol. 30(2), pages 501-546, April.
    4. Frédéric Abergel & Rémi Tachet, 2010. "A nonlinear partial integro-differential equation from mathematical finance," Post-Print hal-00611962, HAL.
    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. Martin Larsson & Shukun Long, 2024. "Markovian projections for It\^o semimartingales with jumps," Papers 2403.15980, arXiv.org.
    2. Ivan Guo & Grégoire Loeper & Shiyi Wang, 2022. "Calibration of local‐stochastic volatility models by optimal transport," Mathematical Finance, Wiley Blackwell, vol. 32(1), pages 46-77, January.
    3. Christoph Reisinger & Maria Olympia Tsianni, 2023. "Convergence of the Euler--Maruyama particle scheme for a regularised McKean--Vlasov equation arising from the calibration of local-stochastic volatility models," Papers 2302.00434, arXiv.org, revised Aug 2023.
    4. Masahiko Egami & Rusudan Kevkhishvili, 2020. "Time reversal and last passage time of diffusions with applications to credit risk management," Finance and Stochastics, Springer, vol. 24(3), pages 795-825, July.
    5. Maxim Bichuch & Agostino Capponi & Stephan Sturm, 2016. "Arbitrage-Free XVA," Papers 1608.02690, arXiv.org.
    6. Nicola Bruti-Liberati & Christina Nikitopoulos-Sklibosios & Eckhard Platen & Erik Schlögl, 2009. "Alternative Defaultable Term Structure Models," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 16(1), pages 1-31, March.
    7. Ying Jiao, 2009. "Multiple defaults and contagion risks," Working Papers hal-00441500, HAL.
    8. Egami, Masahiko & Kevkhishvili, Rusudan, 2025. "On decomposition of the last passage time of diffusions," Stochastic Processes and their Applications, Elsevier, vol. 182(C).
    9. Duffie, Darrell, 2005. "Credit risk modeling with affine processes," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2751-2802, November.
    10. Kardaras, Constantinos, 2015. "On the stochastic behaviour of optional processes up to random times," LSE Research Online Documents on Economics 64965, London School of Economics and Political Science, LSE Library.
    11. Junchi Ma & Mobolaji Ogunsolu & Jinniao Qiu & Ayşe Deniz Sezer, 2023. "Credit risk pricing in a consumption‐based equilibrium framework with incomplete accounting information," Mathematical Finance, Wiley Blackwell, vol. 33(3), pages 666-708, July.
    12. Blanchet-Scalliet, Christophette & El Karoui, Nicole & Martellini, Lionel, 2005. "Dynamic asset pricing theory with uncertain time-horizon," Journal of Economic Dynamics and Control, Elsevier, vol. 29(10), pages 1737-1764, October.
    13. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    14. Ivan Guo & Gregoire Loeper, 2018. "Path Dependent Optimal Transport and Model Calibration on Exotic Derivatives," Papers 1812.03526, arXiv.org, revised Sep 2020.
    15. Aksamit, Anna & Jeanblanc, Monique & Rutkowski, Marek, 2019. "Integral representations of martingales for progressive enlargements of filtrations," Stochastic Processes and their Applications, Elsevier, vol. 129(4), pages 1229-1258.
    16. Ying Jiao, 2009. "Multiple defaults and contagion risks," Papers 0912.3132, arXiv.org.
    17. Fairouz Tchier & Ioannis Dassios & Ferdous Tawfiq & Lakhdar Ragoub, 2021. "On the Approximate Solution of Partial Integro-Differential Equations Using the Pseudospectral Method Based on Chebyshev Cardinal Functions," Mathematics, MDPI, vol. 9(3), pages 1-14, February.
    18. Ashkan Nikeghbali & Eckhard Platen, 2008. "On Honest Times in Financial Modeling," Research Paper Series 229, Quantitative Finance Research Centre, University of Technology, Sydney.
    19. Mathias Beiglbock & George Lowther & Gudmund Pammer & Walter Schachermayer, 2021. "Faking Brownian motion with continuous Markov martingales," Papers 2109.12927, arXiv.org.
    20. Ashkan Nikeghbali & Eckhard Platen, 2013. "A reading guide for last passage times with financial applications in view," Finance and Stochastics, Springer, vol. 17(3), pages 615-640, July.

    More about this item

    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:2412.04589. 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.