Calibration and Backtesting of the Heston Model for Counterparty Credit Risk

Innocentis, Marco de; Levendorskiı̌, Sergei

doi:10.2139/ssrn.2757008

Cited by 9 publications

(6 citation statements)

References 13 publications

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“…The methodology can be also applied to evaluation of special functions [29], the Wiener-Hopf factors, calculation of distributions of the infimum and supremum of Lévy processes, pricing of path-dependent options, Monte-Carlo simulations of options with barrier features, pricing in models of Ornstein-Uhlenbeck type, and in many other cases. The efficiency of the calibration procedure of the Heston model in [20,21] can also be improved. To apply the sinh-acceleration to pricing in regime-switching models, it suffices to use matrix operations instead of the scalar ones (and, naturally, study the region where the matrix functions and their reciprocals are analytic; formally, the scheme remains the same).…”

Section: Discussionmentioning

confidence: 99%

“…where ω ∈ R, σ > 0, α > 1, was systematically used in a series of papers [7,28,6,32,13,5,30,8,31,20,21]. In the working paper [29], it was suggested to use the sinh-acceleration η = sinh(ay)/a with integration over the real line after the fractional-parabolic change of variables has been made.…”

Section: Introductionmentioning

confidence: 99%

“…Depending on the sign of ω, the new contour of integration L ω 1 ,ω,b is deformed either upward or downward, and the deformed contours enjoy properties similar to the properties of the contours in [7,28,6,32,13,5,30,8,31,20,21,29]. The number of terms of the simplified trapezoid rule is approximately the same as in [29] (and smaller than in [7,28,6,32,13,5,30,8,31,20,21], where thousands of terms are needed in some cases) but the number of elementary operations needed to calculate individual terms decreases. The general scheme is simpler than the one in [29].…”

Section: Introductionmentioning

confidence: 99%

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Sinh-Acceleration: Efficient Evaluation of Probability Distributions, Option Pricing, and Monte Carlo Simulations

Boyarchenko

Levendorskiı̌

2019

Int. J. Theor. Appl. Finan.

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Characteristic functions of several popular classes of distributions and processes admit analytic continuation into unions of strips and open coni around R ⊂ C. The Fourier transform techniques reduces calculation of probability distributions and option prices to evaluation of integrals whose integrands are analytic in domains enjoying these properties. In the paper, we suggest to use changes of variables of the form ξ = √ −1ω1 + b sinh( √ −1ω + y) and the simplified trapezoid rule to evaluate the integrals accurately and fast. We formulate the general scheme, and apply the scheme for calculation probability distributions and pricing European options in Lévy models, the Heston model, the CIR model, and a Lévy model with the CIR-subordinator. We outline applications to fast and accurate calibration procedures and Monte Carlo simulations in Lévy models, regime switching Lévy models that can account for stochastic drift, volatility and skewness, and the Heston model. For calculation of quantiles in the tails using the Newton or bisection method, it suffices to precalculate several hundred of values of the characteristic exponent at points of an appropriate grid (conformal principal components) and use these values in formulas for cpdf and pdf.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Sinh-Acceleration: Efficient Evaluation of Probability Distributions, Option Pricing, and Monte Carlo Simulations

Boyarchenko

Levendorskiı̌

2019

Int. J. Theor. Appl. Finan.

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“…See Levendorski ȋ (2011, 2014); Levendorski ȋ (2016b) for the theoretical analysis and examples. As explained in Innocentis and Levendorski ȋ (2016); Boyarchenko and Levendorski ȋ (2015), an inaccurate pricing procedure used for calibration purposes will not recognize the correct parameter set (sundial calibration) and will find a local minimum where the true calibration error and error of the method almost cancel one another: the calibration procedure will see ghosts at the boundary of the region in the parameter space where the numerical method performs reasonably well (ghost calibration). If a method is rather inaccurate, this region is small, and, therefore, the calibration "succeeds" to find a presumably good set of the parameters of the model very fast.…”

mentioning

confidence: 99%

SINH-acceleration for B-spline projection with Option Pricing Applications

Boyarchenko¹,

Levendorskiu{i}²,

Kirkby³

et al. 2021

Preprint

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We clarify the relations among different Fourier-based approaches to option pricing, and improve the B-spline probability density projection method using the sinh-acceleration technique. This allows us to efficiently separate the control of different sources of errors better than the FFT-based realization allows; in many cases, the CPU time decreases as well. We demonstrate the improvement of the B-spline projection method through several numerical experiments in option pricing, including European and barrier options, where the SINH acceleration technique proves to be robust and accurate.

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“…However, even in this case, an accurate and fast option pricing is not trivial, and serious errors can result, for options of short and long maturity especially. See [21,22] for examples in the context of calibration of the Heston model, and [27,8] for efficient numerical integration procedures. In the case of models of the CIR type, difficulties for accurate calculations are even more serious [28,8].…”

mentioning

confidence: 99%

Gauge Transformations in the Dual Space, and Pricing and Estimation in the Long Run in Affine Jump-Diffusion Models

Boyarchenko

Levendorskiı̌

2019

SSRN Journal

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We suggest a simple reduction of pricing European options in affine jump-diffusion models to pricing options with modified payoffs in diffusion models. The procedure is based on the conjugation of the infinitesimal generator of the model with an operator of the form e iΦ(−i∂x) (gauge transformation in the dual space). A general procedure for the calculation of the function Φ is given, with examples. As applications, we consider pricing in jumpdiffusion models and their subordinated versions using the eigenfunction expansion technique, and estimation of the extremely rare jumps component. The beliefs of the market about yet unobserved extreme jumps and pricing kernel can be recovered: the market prices allow one to see "the shape of things to come".

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Calibration and Backtesting of the Heston Model for Counterparty Credit Risk

Cited by 9 publications

References 13 publications

Sinh-Acceleration: Efficient Evaluation of Probability Distributions, Option Pricing, and Monte Carlo Simulations

Sinh-Acceleration: Efficient Evaluation of Probability Distributions, Option Pricing, and Monte Carlo Simulations

SINH-acceleration for B-spline projection with Option Pricing Applications

Gauge Transformations in the Dual Space, and Pricing and Estimation in the Long Run in Affine Jump-Diffusion Models

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