IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2210.15343.html
   My bibliography  Save this paper

Change of measure in a Heston-Hawkes stochastic volatility model

Author

Listed:
  • David R. Ba~nos
  • Salvador Ortiz-Latorre
  • Oriol Zamora Font

Abstract

We consider the stochastic volatility model obtained by adding a compound Hawkes process to the volatility of the well-known Heston model. A Hawkes process is a self-exciting counting process with many applications in mathematical finance, insurance, epidemiology, seismology and other fields. We prove a general result on the existence of a family of equivalent (local) martingale measures. We apply this result to a particular example where the sizes of the jumps are exponentially distributed.

Suggested Citation

  • David R. Ba~nos & Salvador Ortiz-Latorre & Oriol Zamora Font, 2022. "Change of measure in a Heston-Hawkes stochastic volatility model," Papers 2210.15343, arXiv.org.
    • Handle: RePEc:arx:papers:2210.15343
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2210.15343
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Chernov, Mikhail & Ghysels, Eric, 2000. "A study towards a unified approach to the joint estimation of objective and risk neutral measures for the purpose of options valuation," Journal of Financial Economics, Elsevier, vol. 56(3), pages 407-458, June.
    2. Torben G. Andersen & Luca Benzoni & Jesper Lund, 2002. "An Empirical Investigation of Continuous‐Time Equity Return Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1239-1284, June.
    3. Bo Martin Bibby & Michael SÛrensen, 1996. "A hyperbolic diffusion model for stock prices (*)," Finance and Stochastics, Springer, vol. 1(1), pages 25-41.
    4. Aurélien Alfonsi, 2015. "Affine Diffusions and Related Processes: Simulation, Theory and Applications," Post-Print hal-03127212, HAL.
    5. Tina Hviid Rydberg, 1999. "Generalized Hyperbolic Diffusion Processes with Applications in Finance," Mathematical Finance, Wiley Blackwell, vol. 9(2), pages 183-201, April.
    6. Tina Hviid Rydberg, 1997. "A note on the existence of unique equivalent martingale measures in a Markovian setting," Finance and Stochastics, Springer, vol. 1(3), pages 251-257.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. David R. Ba~nos & Salvador Ortiz-Latorre & Oriol Zamora Font, 2023. "Thiele's PIDE for unit-linked policies in the Heston-Hawkes stochastic volatility model," Papers 2309.03541, arXiv.org, revised Feb 2024.

    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. H. Peter Boswijk & Roger J. A. Laeven & Evgenii Vladimirov, 2022. "Estimating Option Pricing Models Using a Characteristic Function-Based Linear State Space Representation," Papers 2210.06217, arXiv.org.
    2. Henri Bertholon & Alain Monfort & Fulvio Pegoraro, 2006. "Pricing and Inference with Mixtures of Conditionally Normal Processes," Working Papers 2006-28, Center for Research in Economics and Statistics.
    3. Chernov, Mikhail & Graveline, Jeremy & Zviadadze, Irina, 2018. "Crash Risk in Currency Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 53(1), pages 137-170, February.
    4. Zeng, Yan & Li, Danping & Chen, Zheng & Yang, Zhou, 2018. "Ambiguity aversion and optimal derivative-based pension investment with stochastic income and volatility," Journal of Economic Dynamics and Control, Elsevier, vol. 88(C), pages 70-103.
    5. Liu, Jun & Pan, Jun, 2003. "Dynamic derivative strategies," Journal of Financial Economics, Elsevier, vol. 69(3), pages 401-430, September.
    6. Bandi, F.M. & Renò, R., 2016. "Price and volatility co-jumps," Journal of Financial Economics, Elsevier, vol. 119(1), pages 107-146.
    7. Nenghui Kuang & Huantian Xie, 2015. "Sequential Maximum Likelihood Estimation for the Hyperbolic Diffusion Process," Methodology and Computing in Applied Probability, Springer, vol. 17(2), pages 373-381, June.
    8. Christoffersen, Peter & Jacobs, Kris & Ornthanalai, Chayawat & Wang, Yintian, 2008. "Option valuation with long-run and short-run volatility components," Journal of Financial Economics, Elsevier, vol. 90(3), pages 272-297, December.
    9. Neumann, Maximilian & Prokopczuk, Marcel & Wese Simen, Chardin, 2016. "Jump and variance risk premia in the S&P 500," Journal of Banking & Finance, Elsevier, vol. 69(C), pages 72-83.
    10. Qian Han & Calum G. Turvey, 2013. "A Robust Equilibrium Relationship between Market Prices of Risks and Risk Aversion in Dynamically Complete Stochastic," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    11. Bondarenko, Oleg, 2014. "Variance trading and market price of variance risk," Journal of Econometrics, Elsevier, vol. 180(1), pages 81-97.
    12. An Chen & Thai Nguyen & Manuel Rach, 2021. "A collective investment problem in a stochastic volatility environment: The impact of sharing rules," Annals of Operations Research, Springer, vol. 302(1), pages 85-109, July.
    13. Neil Shephard & Torben Andersen, 2008. "Stochastic Volatility: Origins and Overview," Economics Papers 2008-W04, Economics Group, Nuffield College, University of Oxford.
    14. Veiga, Helena, 2006. "A two factor long memory stochastic volatility model," DES - Working Papers. Statistics and Econometrics. WS ws061303, Universidad Carlos III de Madrid. Departamento de Estadística.
    15. Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003. "Alternative models for stock price dynamics," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 225-257.
    16. Veiga, Helena, 2006. "Volatility forecasts: a continuous time model versus discrete time models," DES - Working Papers. Statistics and Econometrics. WS ws062509, Universidad Carlos III de Madrid. Departamento de Estadística.
    17. Chernov, Mikhail & Graveline, Jeremy & Zviadadze, Irina, 2012. "Sources of Risk in Currency Returns," CEPR Discussion Papers 8745, C.E.P.R. Discussion Papers.
    18. Alfonsi, Aurélien & Kebaier, Ahmed & Rey, Clément, 2016. "Maximum likelihood estimation for Wishart processes," Stochastic Processes and their Applications, Elsevier, vol. 126(11), pages 3243-3282.
    19. Peter Christoffersen & Steven Heston & Kris Jacobs, 2009. "The Shape and Term Structure of the Index Option Smirk: Why Multifactor Stochastic Volatility Models Work So Well," Management Science, INFORMS, vol. 55(12), pages 1914-1932, December.
    20. Carverhill, Andrew & Luo, Dan, 2023. "A Bayesian analysis of time-varying jump risk in S&P 500 returns and options," Journal of Financial Markets, Elsevier, vol. 64(C).

    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:2210.15343. 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.