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The pricing of credit default swaps under a generalized mixed fractional Brownian motion

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  • He, Xinjiang
  • Chen, Wenting

Abstract

In this paper, we consider the pricing of the CDS (credit default swap) under a GMFBM (generalized mixed fractional Brownian motion) model. As the name suggests, the GMFBM model is indeed a generalization of all the FBM (fractional Brownian motion) models used in the literature, and is proved to be able to effectively capture the long-range dependence of the stock returns. To develop the pricing mechanics of the CDS, we firstly derive a sufficient condition for the market modeled under the GMFBM to be arbitrage free. Then under the risk-neutral assumption, the CDS is fairly priced by investigating the two legs of the cash flow involved. The price we obtained involves elementary functions only, and can be easily implemented for practical purpose. Finally, based on numerical experiments, we analyze quantitatively the impacts of different parameters on the prices of the CDS. Interestingly, in comparison with all the other FBM models documented in the literature, the results produced from the GMFBM model are in a better agreement with those calculated from the classical Black–Scholes model.

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  • He, Xinjiang & Chen, Wenting, 2014. "The pricing of credit default swaps under a generalized mixed fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 404(C), pages 26-33.
    • Handle: RePEc:eee:phsmap:v:404:y:2014:i:c:p:26-33
    DOI: 10.1016/j.physa.2014.02.046
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    Cited by:

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    3. Ballestra, Luca Vincenzo & Pacelli, Graziella & Radi, Davide, 2016. "A very efficient approach for pricing barrier options on an underlying described by the mixed fractional Brownian motion," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 240-248.
    4. Ahmadian, D. & Ballestra, L.V., 2020. "Pricing geometric Asian rainbow options under the mixed fractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).
    5. Ballestra, Luca Vincenzo & Pacelli, Graziella & Radi, Davide, 2016. "A very efficient approach to compute the first-passage probability density function in a time-changed Brownian model: Applications in finance," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 463(C), pages 330-344.
    6. Yang, Zhaoqiang, 2020. "Default probability of American lookback option in a mixed jump-diffusion model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 540(C).
    7. Foad Shokrollahi & Davood Ahmadian & Luca Vincenzo Ballestra, 2021. "Actuarial strategy for pricing Asian options under a mixed fractional Brownian motion with jumps," Papers 2105.06999, arXiv.org.
    8. Arias-Calluari, Karina & Najafi, Morteza. N. & Harré, Michael S. & Tang, Yaoyue & Alonso-Marroquin, Fernando, 2022. "Testing stationarity of the detrended price return in stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 587(C).
    9. Chen, Wenting & Yan, Bowen & Lian, Guanghua & Zhang, Ying, 2016. "Numerically pricing American options under the generalized mixed fractional Brownian motion model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 180-189.
    10. Zhang, Xili & Xiao, Weilin, 2017. "Arbitrage with fractional Gaussian processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 471(C), pages 620-628.
    11. Shokrollahi, F. & Ahmadian, D. & Ballestra, L.V., 2024. "Pricing Asian options under the mixed fractional Brownian motion with jumps," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 226(C), pages 172-183.

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