Calibration and Backtesting of the Heston Model for Counterparty Credit Risk

11 Pages Posted: 1 May 2016 Last revised: 8 Jan 2018

See all articles by Marco de Innocentis

Marco de Innocentis

Credit Suisse Securities (Europe) Limited; University of Leicester

Sergei Levendorskii

Calico Science Consulting

Date Written: April 30, 2016


We describe a fast new method for the market implied calibration of the Heston (1993) model for equity, based on an improved version of the parabolic pricing algorithm of Levendorskii (2012). This pricing method, when used in the calibration, is much faster and more accurate, and better reproduces the implied volatilities, than alternative methods which are popular with practitioners. As such, it is suitable for use in a typical IMM counterparty risk engine. We also show that the Heston model, calibrated to fit the implied volatility surfaces between January 2010 and December 2016, performs well in historical backtesting for a range of exception counting and distributional tests across multiple time horizons. Our benchmarking tests were designed in accordance to the Federal Reserve's Supervisory Guidance Letter SR-11-7 (2011), which has become a worldwide standard for model development and validation.

Keywords: Heston model, calibration, benchmarking, SR-11-7, backtest, COS, FFT, counterparty risk, CVA

JEL Classification: G12, C63

Suggested Citation

de Innocentis, Marco and Levendorskii, Sergei Z., Calibration and Backtesting of the Heston Model for Counterparty Credit Risk (April 30, 2016). Available at SSRN: or

Marco De Innocentis (Contact Author)

Credit Suisse Securities (Europe) Limited ( email )

1 Cabot Square
London, E14 4QJ
United Kingdom

University of Leicester ( email )

Department of Mathematics
University Road
Leicester, LE1 7RG
United Kingdom

Sergei Z. Levendorskii

Calico Science Consulting ( email )

Austin, TX
United States

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