IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2012.01257.html
   My bibliography  Save this paper

Error estimates for discrete approximations of game options with multivariate diffusion asset prices

Author

Listed:
  • Yuri Kifer

Abstract

We obtain error estimates for strong approximations of a diffusion with a diffusion matrix $\sigma$ and a drift b by the discrete time process defined recursively X_N((n+1)/N) = X_N(n/N)+N^{1/2}\sigma(X_N(n/N))\xi(n+1)+N^{-1}b(XN(n/N)); where \xi(n); n\geq 1 are i.i.d. random vectors, and apply this in order to approximate the fair price of a game option with a diffusion asset price evolution by values of Dynkin's games with payoffs based on the above discrete time processes. This provides an effective tool for computations of fair prices of game options with path dependent payoffs in a multi asset market with diffusion evolution.

Suggested Citation

  • Yuri Kifer, 2020. "Error estimates for discrete approximations of game options with multivariate diffusion asset prices," Papers 2012.01257, arXiv.org, revised Dec 2021.
    • Handle: RePEc:arx:papers:2012.01257
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2012.01257
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Yuri Kifer, 2006. "Error estimates for binomial approximations of game options," Papers math/0607123, arXiv.org.
    2. He, Hua, 1990. "Convergence from Discrete- to Continuous-Time Contingent Claims Prices," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 523-546.
    3. Yan Dolinsky, 2009. "Applications of weak convergence for hedging of game options," Papers 0908.3661, arXiv.org, revised Nov 2010.
    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. Buss, Adrian, 2013. "Capital controls and international financial stability: a dynamic general equilibrium analysis in incomplete markets," Working Paper Series 1578, European Central Bank.
    2. Detemple, Jerome & Sundaresan, Suresh, 1999. "Nontraded Asset Valuation with Portfolio Constraints: A Binomial Approach," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 835-872.
    3. Hyong-chol O & Song-San Jo, 2019. "Variational inequality for perpetual American option price and convergence to the solution of the difference equation," Papers 1903.05189, arXiv.org.
    4. Rüdiger Frey & Alexander Stremme, 1997. "Market Volatility and Feedback Effects from Dynamic Hedging," Mathematical Finance, Wiley Blackwell, vol. 7(4), pages 351-374, October.
    5. Wael Bahsoun & Pawel Góra & Silvia Mayoral & Manuel Morales, 2006. "Random Dynamics and Finance: Constructing Implied Binomial Trees from a Predetermined Stationary Den," Faculty Working Papers 13/06, School of Economics and Business Administration, University of Navarra.
    6. Hranaiova, Jana & Tomek, William G., 2000. "Delivery Option In Futures Contracts And Basis Behavior At Contract Maturity," 2000 Annual meeting, July 30-August 2, Tampa, FL 21732, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    7. Leitner, Johannes, 2000. "Convergence of Arbitrage-free Discrete Time Markovian Market Models," CoFE Discussion Papers 00/07, University of Konstanz, Center of Finance and Econometrics (CoFE).
    8. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.
    9. Angel León & Enrique Sentana, 1997. "Pricing Options on Assets with Predictable White Noise Returns," FMG Discussion Papers dp267, Financial Markets Group.
    10. Garcia, Diego, 2003. "Convergence and Biases of Monte Carlo estimates of American option prices using a parametric exercise rule," Journal of Economic Dynamics and Control, Elsevier, vol. 27(10), pages 1855-1879, August.
    11. Andrea Beltratti & Paolo Colla, 2007. "A portfolio-based evaluation of affine term structure models," Annals of Operations Research, Springer, vol. 151(1), pages 193-222, April.
    12. Guo, Peidong & Zhang, Jizhou & Wang, Qian, 2020. "Path-dependent game options with Asian features," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
    13. Valeri Zakamouline, 2005. "A unified approach to portfolio optimization with linear transaction costs," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 62(2), pages 319-343, November.
    14. Péter Juhász & Nóra Felföldi-Szűcs, 2022. "Financing Cooperative Supply Chain Members—The Bank’s Perspective," Risks, MDPI, vol. 10(7), pages 1-17, July.
    15. Valeri Zakamouline, 2003. "European Option Pricing and Hedging with both Fixed and Proportional Transaction Costs," Finance 0311009, University Library of Munich, Germany.
    16. Marcos Escobar & Paul Kriebel & Markus Wahl & Rudi Zagst, 2019. "Portfolio optimization under Solvency II," Annals of Operations Research, Springer, vol. 281(1), pages 193-227, October.
    17. Antje Mahayni, 2003. "Effectiveness of Hedging Strategies under Model Misspecification and Trading Restrictions," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(05), pages 521-552.
    18. Leisen, Dietmar P. J., 1999. "The random-time binomial model," Journal of Economic Dynamics and Control, Elsevier, vol. 23(9-10), pages 1355-1386, September.
    19. Carlos de Lamare Bastian-Pinto & Alexandre Paula Silva Ramos & Luiz de Magalhães Ozorio & Luiz Eduardo Teixeira Brandão, 2015. "Uncertainty and Flexibility in the Brazilian Beef Livestock Sector: the Value of the Confinement Option," Brazilian Business Review, Fucape Business School, vol. 12(6), pages 100-120, November.
    20. Victor DeMiguel & Raman Uppal, 2005. "Portfolio Investment with the Exact Tax Basis via Nonlinear Programming," Management Science, INFORMS, vol. 51(2), pages 277-290, February.

    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:2012.01257. 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.