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Cva And Vulnerable Options In Stochastic Volatility Models

Author

Listed:
  • E. ALÒS

    (Department of Economics and Business, University Pompeu Fabra, and Barcelona GSE, Barcelona, Spain)

  • F. ANTONELLI

    (Department of Information Engineering, Computer Science and Mathematics, University of L’Aquila, L’Aquila Italy)

  • A. RAMPONI

    (Department of Economics and Finance, University of Rome Tor Vergata, Rome, Italy)

  • S. SCARLATTI

    (Department of Enterprise Engineering, University of Rome Tor Vergata, Rome, Italy)

Abstract

This work aims to provide an efficient method to evaluate the Credit Value Adjustment (CVA) for a vulnerable European option, which is an option subject to some default event concerning the issuer solvability. Financial options traded in OTC markets are of this type. In particular, we compute the CVA in some popular stochastic volatility models such as SABR, Hull et al., which have proven to fit quite well market derivatives prices, admitting correlation with the default event. This choice covers the relevant case of Wrong Way Risk (WWR) when a credit deterioration determines an increase in the claim value. Contrary to the structural modeling adopted in [G. Wang, X. Wang & K. Zhu (2017) Pricing vulnerable options with stochastic volatility, Physica A 485, 91–103; C. Ma, S. Yue & Y. Ma (2020) Pricing vulnerable options with Stochastic volatility and Stochastic interest rate, Computational Economics 56, 391–429], we use the reduced-form intensity-based approach to provide an explicit representation formula for the vulnerable option price and related CVA. Later, we specialize the evaluation formula and construct its approximation for the three models mentioned above. Assuming a CIR model for the default intensity process, we run a numerical study to test our approximation, comparing it with Monte Carlo simulations. The results show that for moderate values of the correlation and maturities not exceeding one year, the approximation is very satisfactory as of accuracy and computational time.

Suggested Citation

  • E. Alòs & F. Antonelli & A. Ramponi & S. Scarlatti, 2021. "Cva And Vulnerable Options In Stochastic Volatility Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 24(02), pages 1-34, March.
    • Handle: RePEc:wsi:ijtafx:v:24:y:2021:i:02:n:s0219024921500102
    DOI: 10.1142/S0219024921500102
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    1. BRIGO, Damiano & VRINS, Frédéric, 2018. "Disentangling wrong-way risk: pricing credit valuation adjustment via change of measures," European Journal of Operational Research, Elsevier, vol. 269(3), pages 1154-1164.
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    Cited by:

    1. Xingchun Wang, 2022. "Valuing fade-in options with default risk in Heston–Nandi GARCH models," Review of Derivatives Research, Springer, vol. 25(1), pages 1-22, April.
    2. Wang, Xingchun & Zhang, Han, 2022. "Pricing basket spread options with default risk under Heston–Nandi GARCH models," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    3. Alòs, Elisa & Antonelli, Fabio & Ramponi, Alessandro & Scarlatti, Sergio, 2023. "CVA in fractional and rough volatility models," Applied Mathematics and Computation, Elsevier, vol. 442(C).
    4. Alessandro Ramponi, 2022. "Spread Option Pricing in Regime-Switching Jump Diffusion Models," Mathematics, MDPI, vol. 10(9), pages 1-15, May.
    5. Elisa Al`os & Fabio Antonelli & Alessandro Ramponi & Sergio Scarlatti, 2022. "CVA in fractional and rough volatility models," Papers 2204.11554, arXiv.org.

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