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Smile and default: the role of stochastic volatility and interest rates in counterparty credit risk

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  • S. Simaitis
  • C. S. L. de Graaf
  • N. Hari
  • D. Kandhai

Abstract

In this research, we investigate the impact of stochastic volatility and interest rates on counterparty credit risk (CCR) for FX derivatives. To achieve this we analyse two real-life cases in which the market conditions are different, namely during the 2008 credit crisis where risks are high and a period after the crisis in 2014, where volatility levels are low. The Heston model is extended by adding two Hull–White components which are calibrated to fit the EURUSD volatility surfaces. We then present future exposure profiles and credit value adjustments (CVAs) for plain vanilla cross-currency swaps (CCYS), barrier and American options and compare the different results when Heston-Hull–White-Hull–White or Black–Scholes dynamics are assumed. It is observed that the stochastic volatility has a significant impact on all the derivatives. For CCYS, some of the impact can be reduced by allowing for time-dependent variance. We further confirmed that Barrier options exposure and CVA is highly sensitive to volatility dynamics and that American options’ risk dynamics are significantly affected by the uncertainty in the interest rates.

Suggested Citation

  • S. Simaitis & C. S. L. de Graaf & N. Hari & D. Kandhai, 2016. "Smile and default: the role of stochastic volatility and interest rates in counterparty credit risk," Quantitative Finance, Taylor & Francis Journals, vol. 16(11), pages 1725-1740, November.
    • Handle: RePEc:taf:quantf:v:16:y:2016:i:11:p:1725-1740
    DOI: 10.1080/14697688.2016.1176240
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    References listed on IDEAS

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    1. Fang, Fang & Oosterlee, Kees, 2008. "A Novel Pricing Method For European Options Based On Fourier-Cosine Series Expansions," MPRA Paper 9319, University Library of Munich, Germany.
    2. Rehez Ahlip & Marek Rutkowski, 2013. "Pricing of foreign exchange options under the Heston stochastic volatility model and CIR interest rates," Quantitative Finance, Taylor & Francis Journals, vol. 13(6), pages 955-966, May.
    3. Lech A. Grzelak & Cornelis W. Oosterlee, 2012. "On Cross-Currency Models with Stochastic Volatility and Correlated Interest Rates," Applied Mathematical Finance, Taylor & Francis Journals, vol. 19(1), pages 1-35, February.
    4. Carl Chiarella & Boda Kang & Gunter H. Meyer, 2010. "The Evaluation Of Barrier Option Prices Under Stochastic Volatility," Research Paper Series 266, Quantitative Finance Research Centre, University of Technology, Sydney.
    5. Lech Grzelak & Cornelis Oosterlee & Sacha Van Weeren, 2011. "The affine Heston model with correlated Gaussian interest rates for pricing hybrid derivatives," Quantitative Finance, Taylor & Francis Journals, vol. 11(11), pages 1647-1663.
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    Cited by:

    1. T. van der Zwaard & L. A. Grzelak & C. W. Oosterlee, 2024. "On the Hull-White model with volatility smile for Valuation Adjustments," Papers 2403.14841, arXiv.org.
    2. Wang, Lei & Li, Shouwei & Chen, Tingqiang, 2019. "Investor behavior, information disclosure strategy and counterparty credit risk contagion," Chaos, Solitons & Fractals, Elsevier, vol. 119(C), pages 37-49.

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