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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
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    References listed on IDEAS

    as
    1. 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.
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    5. Jamshidian, Farshid, 1989. " An Exact Bond Option Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 205-209, March.
    6. 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.
    7. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
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