IDEAS home Printed from https://ideas.repec.org/h/spr/isochp/978-0-387-71163-8_4.html
   My bibliography  Save this book chapter

Pricing Options and Variance Swaps in Markov-Modulated Brownian Markets

In: Hidden Markov Models in Finance

Author

Listed:
  • Robert J. Elliott

    (University of Calgary)

  • Anatoliy V. Swishchuk

    (University of Calgary)

Abstract

Summary A Markov-modulated market consists of a riskless asset or bond, B, and a risky asset or stock, S, whose dynamics depend on Markov process x. We study the pricing of options and variance swaps in such markets. Using the martingale characterization of Markov processes, we note the incompleteness of Markov-modulated markets and find the minimal martingale measure. Black-Scholes formulae for Markov-modulated markets with or without jumps are derived. Perfect hedging in a Markov-modulated Brownian and a fractional Brownian market is not possible as the market is incomplete. Following the idea proposed by Föllmer and Sondermann [13] and Föllmer and Schweizer [12]) we look for the strategy which locally minimizes the risk. The residual risk processes are determined in these situations. Variance swaps for stochastic volatility driven by Markov process are also studied.

Suggested Citation

  • Robert J. Elliott & Anatoliy V. Swishchuk, 2007. "Pricing Options and Variance Swaps in Markov-Modulated Brownian Markets," International Series in Operations Research & Management Science, in: Rogemar S. Mamon & Robert J. Elliott (ed.), Hidden Markov Models in Finance, chapter 4, pages 45-68, Springer.
    • Handle: RePEc:spr:isochp:978-0-387-71163-8_4
    DOI: 10.1007/0-387-71163-5_4
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    Citations

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


    Cited by:

    1. Zhengyuan Gao & Christian M. Hafner, 2019. "Looking Backward and Looking Forward," Econometrics, MDPI, vol. 7(2), pages 1-24, June.
    2. Subhojit Biswas & Diganta Mukherjee & Indranil SenGupta, 2020. "Multi-asset Generalised Variance Swaps in Barndorff-Nielsen and Shephard model," Papers 2011.13474, arXiv.org.
    3. Subhojit Biswas & Diganta Mukherjee, 2019. "A Proposal for Multi-asset Generalised Variance Swaps," Papers 1908.03899, arXiv.org.
    4. Yonit Barron, 2022. "A probabilistic approach to the stochastic fluid cash management balance problem," Annals of Operations Research, Springer, vol. 312(2), pages 607-645, May.
    5. Anatoliy Swishchuk, 2013. "Modeling and Pricing of Swaps for Financial and Energy Markets with Stochastic Volatilities," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8660, September.
    6. David Saunders & Luis Seco & Markus Senn, 2020. "Price of liquidity in the reinsurance of fund returns," Papers 2011.13268, arXiv.org.
    7. Shen, Yang & Siu, Tak Kuen, 2013. "Pricing bond options under a Markovian regime-switching Hull–White model," Economic Modelling, Elsevier, vol. 30(C), pages 933-940.
    8. Barron, Yonit, 2023. "A stochastic card balance management problem with continuous and batch-type bilateral transactions," Operations Research Perspectives, Elsevier, vol. 10(C).

    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:spr:isochp:978-0-387-71163-8_4. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.