IDEAS home Printed from https://ideas.repec.org/p/bcb/wpaper/409.html
   My bibliography  Save this paper

A Discrete Monitoring Method for Pricing Asian Interest Rate Options

Author

Listed:
  • Allan Jonathan da Silva
  • Jack Baczynskiy
  • José Valentim M. Vicente

Abstract

As determined by the BM&FBovespa standards, the ID index is built up discretely according to overnight DI rate. We addressed the IDI Call Option Pricing problem using this discretely compounded hypothesis in lieu of the continuous updated case found in the literature. Our method converges to the benchmark (which refers to the exact price considering the discretely compounded hypothesis). This is not possible for any short rate modeling framework which adopts IDI continuously compounded hypothesis. It is noteworthy that the benchmark prices as well as the prices under the discretely compounded hypothesis with a reasonable number of mesh points are always cheaper than those of the continuously compounded case. In addition, we introduced a general purpose version of a classical finite difference scheme which provides an spurious oscillation free solution of the PDE to obtain an approximate price of the option.

Suggested Citation

  • Allan Jonathan da Silva & Jack Baczynskiy & José Valentim M. Vicente, 2015. "A Discrete Monitoring Method for Pricing Asian Interest Rate Options," Working Papers Series 409, Central Bank of Brazil, Research Department.
    • Handle: RePEc:bcb:wpaper:409
    as

    Download full text from publisher

    File URL: https://www.bcb.gov.br/content/publicacoes/WorkingPaperSeries/wps409.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Chan, K C, et al, 1992. "An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-1227, July.
    2. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    3. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    4. repec:bla:jfinan:v:44:y:1989:i:1:p:205-09 is not listed on IDEAS
    5. Caio Almeida & Jos� Vicente, 2012. "Term structure movements implicit in Asian option prices," Quantitative Finance, Taylor & Francis Journals, vol. 12(1), pages 119-134, February.
    6. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
    7. Markus Bouziane, 2008. "Pricing Interest-Rate Derivatives," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-77066-4, October.
    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. Takami, Marcelo Yoshio & Tabak, Benjamin Miranda, 2008. "Interest rate option pricing and volatility forecasting: An application to Brazil," Chaos, Solitons & Fractals, Elsevier, vol. 38(3), pages 755-763.
    2. Das, Sanjiv Ranjan, 1998. "A direct discrete-time approach to Poisson-Gaussian bond option pricing in the Heath-Jarrow-Morton model," Journal of Economic Dynamics and Control, Elsevier, vol. 23(3), pages 333-369, November.
    3. 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.
    4. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    5. Carl Chiarella & Xue-Zhong He & Christina Sklibosios Nikitopoulos, 2015. "Derivative Security Pricing," Dynamic Modeling and Econometrics in Economics and Finance, Springer, edition 127, number 978-3-662-45906-5, June.
    6. Collin-Dufresne, Pierre & Goldstein, Robert S. & Jones, Christopher S., 2009. "Can interest rate volatility be extracted from the cross section of bond yields?," Journal of Financial Economics, Elsevier, vol. 94(1), pages 47-66, October.
    7. Juan M. Moraleda & Ton Vorst, 1996. "The Valuation of Interest Rate Derivatives: Empirical Evidence from the Spanish Market," Tinbergen Institute Discussion Papers 96-170/2, Tinbergen Institute.
    8. Falini, Jury, 2010. "Pricing caps with HJM models: The benefits of humped volatility," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1358-1367, December.
    9. Alan De Genaro & Marco Avellaneda, 2018. "Pricing Interest Rate Derivatives Under Monetary Changes," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 21(06), pages 1-28, September.
    10. Duyvesteyn, Johan & de Zwart, Gerben, 2015. "Riding the swaption curve," Journal of Banking & Finance, Elsevier, vol. 59(C), pages 57-75.
    11. Sutthimat, Phiraphat & Mekchay, Khamron & Rujivan, Sanae, 2022. "Closed-form formula for conditional moments of generalized nonlinear drift CEV process," Applied Mathematics and Computation, Elsevier, vol. 428(C).
    12. Allan Jonathan da Silva & Jack Baczynski & José Valentim Machado Vicente, 2020. "Efficient Solutions for Pricing and Hedging Interest Rate Asian Options," Working Papers Series 513, Central Bank of Brazil, Research Department.
    13. Christina Nikitopoulos-Sklibosios, 2005. "A Class of Markovian Models for the Term Structure of Interest Rates Under Jump-Diffusions," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 1-2005, January-A.
    14. Ruijun Bu & Fredj Jawadi & Yuyi Li, 2020. "A multifactor transformed diffusion model with applications to VIX and VIX futures," Econometric Reviews, Taylor & Francis Journals, vol. 39(1), pages 27-53, January.
    15. Kimmel, Robert L., 2004. "Modeling the term structure of interest rates: A new approach," Journal of Financial Economics, Elsevier, vol. 72(1), pages 143-183, April.
    16. Chen, Homing & Hu, Cheng-Feng, 2010. "A relaxed cutting plane algorithm for solving the Vasicek-type forward interest rate model," European Journal of Operational Research, Elsevier, vol. 204(2), pages 343-354, July.
    17. Podolskij, Mark & Vetter, Mathias, 2009. "Bipower-type estimation in a noisy diffusion setting," Stochastic Processes and their Applications, Elsevier, vol. 119(9), pages 2803-2831, September.
    18. Zhao, Zhibiao, 2011. "Nonparametric model validations for hidden Markov models with applications in financial econometrics," Journal of Econometrics, Elsevier, vol. 162(2), pages 225-239, June.
    19. Nicolas Mougeot, "undated". "Credit Spread Specification and the Pricing of Spread Options," FAME Research Paper Series rp14, International Center for Financial Asset Management and Engineering.
    20. Nowman, K. Ben & Sorwar, Ghulam, 2005. "Derivative prices from interest rate models: results for Canada, Hong Kong, and United States," International Review of Financial Analysis, Elsevier, vol. 14(4), pages 428-438.

    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:bcb:wpaper:409. 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: Rodrigo Barbone Gonzalez (email available below). General contact details of provider: https://www.bcb.gov.br/en .

    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.