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On the Interest Rate Derivatives Pricing with Discrete Probability Distribution and Calibration with Genetic Algorithm

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  • Allan Jonathan da Silva
  • Leonardo Fagundes de Mello

Abstract

Bond prices and fixed-income derivatives intricately depend on the ever-evolving landscape of interest rates. This study introduces an exceptionally efficient semi-analytical pricing methodology designed for discretely updated path-dependent interest rate options. Our approach involves the derivation of an analytical solution for the characteristic function of the logarithm of the discretely discounted strike price, enabling the computation of coefficients for the Fourier-cosine series governing the path-dependent option pricing. The distinctive feature of our pricing method lies in the utilization of a modified Skellam probability distribution to model interest rate increments, resulting in a remarkably swift and precise calculation process. Unlike existing solutions for similar pricing challenges, our proposed formula considerably enhances computational efficiency. Moreover, we delve into the influence of central bank monetary decision probabilities on option prices via a comprehensive series of numerical experiments. In an effort to further fine-tune the calibration parameter values for the yield curve, we employ a genetic algorithm, thus contributing to the heightened precision of our pricing model. This research, with its innovative approach, not only refines pricing procedures but also offers valuable insights into the dynamic interplay between monetary policies and fixed-income derivatives.

Suggested Citation

  • Allan Jonathan da Silva & Leonardo Fagundes de Mello, 2024. "On the Interest Rate Derivatives Pricing with Discrete Probability Distribution and Calibration with Genetic Algorithm," International Journal of Economics and Finance, Canadian Center of Science and Education, vol. 16(1), pages 1-42, January.
    • Handle: RePEc:ibn:ijefaa:v:16:y:2024:i:1:p:42
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    References listed on IDEAS

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    1. Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, vol. 106(1), pages 27-65, January.
    2. David K. Backus & Stanley E. Zin, 1993. "Long-memory inflation uncertainty: evidence from the term structure of interest rates," Proceedings, Federal Reserve Bank of Cleveland, pages 681-708.
    3. Xiao, Weilin & Zhang, Weiguo & Zhang, Xili & Chen, Xiaoyan, 2014. "The valuation of equity warrants under the fractional Vasicek process of the short-term interest rate," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 320-337.
    4. Gomes, Orlando & Mendes, Diana A. & Mendes, Vivaldo M., 2008. "Bounded rational expectations and the stability of interest rate policy," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3882-3890.
    5. Fama, Eugene F, 1975. "Short-Term Interest Rates as Predictors of Inflation," American Economic Review, American Economic Association, vol. 65(3), pages 269-282, June.
    6. Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
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    Cited by:

    1. Allan Jonathan da Silva & Jack Baczynski, 2024. "Exploring non-analytical affine jump-diffusion models for path-dependent interest rate derivatives," Computational Management Science, Springer, vol. 21(1), pages 1-32, June.

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    JEL classification:

    • R00 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General - - - General
    • Z0 - Other Special Topics - - General

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