Impact of Multiple-Curve Dynamics in Credit Valuation Adjustments

Bormetti, Giacomo; Brigo, Damiano; Francischello, Marco; Pallavicini, Andrea

doi:10.1007/978-3-319-33446-2_12

Cited by 4 publications

(3 citation statements)

References 26 publications

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“…Moreover, we complement our results with a parameter stability analysis in the case of the CIR-Gamma model, showing a satisfactory degree of stability. We refer to [6,15] for calibration results based on swaption data and to [51] for a calibration approach which relies on ATM European swaption and cap quotes. 6.1.…”

Section: Calibration Analysismentioning

confidence: 99%

“…We take the calibrated parameters from Table 1 as initial guess for a sequence of calibration experiments over a time window from August 2 nd , 2011 up to August 31 st , 2011. 6 The output of the procedure is a time series of calibrated parameters and calibration statistics. First of all, Figure 4 bottom panel shows that the quality of the fit, as measured by the sum of squared implied volatility errors, is subject to minor oscillations along the time window we consider, ranging between 0.0013 and 0.0019.…”

Section: Calibration Analysismentioning

confidence: 99%

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Affine Multiple Yield Curve Models

2016

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We provide a general and tractable framework under which all multiple yield curve modeling approaches based on affine processes, be it short rate, Libor market, or HJM modeling, can be consolidated. We model a numéraire process and multiplicative spreads between Libor rates and simply compounded OIS rates as functions of an underlying affine process. Besides allowing for ordered spreads and an exact fit to the initially observed term structures, this general framework leads to tractable valuation formulas for caplets and swaptions and embeds all existing multi-curve affine models. The proposed approach also gives rise to new developments, such as a short rate type model driven by a Wishart process, for which we derive a closed-form pricing formula for caplets. The empirical performance of two specifications of our framework is illustrated by calibration to market data.2010 Mathematics Subject Classification. 91G30, 91B24, 91B70. JEL Classification E43, G12. Key words and phrases. Multiple yield curves, Libor rate, forward rate agreement, multiplicative spread, affine processes. Acknowledgements. The authors are grateful to two anonymous referees for their valuable comments that helped to significantly improve the paper. 1 Similarly as in [5,28], we denote by Xibor a generic interbank offered rate for unsecured term lending, such as the Libor rate in the London interbank market and the Euribor rate in the Eurozone. While the theoretical framework developed in the present paper applies to generic Xibor rates, the empirical results reported in Section 6 refer to Euribor rates. 1 arXiv:1603.00527v2 [q-fin.MF]

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Section: Calibration Analysismentioning

confidence: 99%

Section: Calibration Analysismentioning

confidence: 99%

Affine Multiple Yield Curve Models

2016

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“…We complement our results with a parameter stability analysis in the case of the CIR‐gamma model, showing a satisfactory degree of stability. We refer to Bormetti, Brigo, Francischello, and Pallavicini () and Crépey, Grbac, Ngor, and Skovmand () for calibration results based on swaption data and to Moreni and Pallavicini () for a calibration approach relying on ATM European swaption and cap quotes.…”

Section: Calibration Analysismentioning

confidence: 99%

Affine multiple yield curve models

Cuchiero

Fontana

Gnoatto

2018

Mathematical Finance

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We provide a general and tractable framework under which all multiple yield curve modeling approaches based on affine processes, be it short rate, Libor market, or Heath-Jarrow-Morton modeling, can be consolidated. We model a numéraire process and multiplicative spreads between Libor rates and simply compounded overnight indexed swap rates as functions of an underlying affine process.Besides allowing for ordered spreads and an exact fit to the initially observed term structures, this general framework leads to tractable valuation formulas for caplets and swaptions and embeds all existing multicurve affine models. The proposed approach also gives rise to new developments, such as a short rate type model driven by a Wishart process, for which we derive a closed-form pricing formula for caplets. The empirical performance of two specifications of our framework is illustrated by calibration to market data. K E Y W O R D Saffine processes, forward rate agreement, Libor rate, multiple yield curves, multiplicative spread J E L C L A S S I F I C A T I O N :E43, G12 568

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Derivative Pricing for a Multi-curve Extension of the Gaussian, Exponentially Quadratic Short Rate Model

Grbac

Meneghello

Runggaldier

2016

Innovations in Derivatives Markets

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The recent financial crisis has led to so-called multi-curve models for the term structure. Here we study a multi-curve extension of short rate models where, in addition to the short rate itself, we introduce short rate spreads. In particular, we consider a Gaussian factor model where the short rate and the spreads are second order polynomials of Gaussian factor processes. This leads to an exponentially quadratic model class that is less well known than the exponentially affine class. In the latter class the factors enter linearly and for positivity one considers square root factor processes. While the square root factors in the affine class have more involved distributions, in the quadratic class the factors remain Gaussian and this leads to various advantages, in particular for derivative pricing. After some preliminaries on martingale modeling in the multi-curve setup, we concentrate on pricing of linear and optional derivatives. For linear derivatives, we exhibit an adjustment factor that allows one to pass from pre-crisis single curve values to the corresponding post-crisis multi-curve values.Keywords Multi-curve models · Short rate models · Short rate spreads · Gaussian exponentially quadratic models · Pricing of linear and optional interest rate derivatives · Riccati equations · Adjustment factors

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Impact of Multiple-Curve Dynamics in Credit Valuation Adjustments

Cited by 4 publications

References 26 publications

Affine Multiple Yield Curve Models

Affine Multiple Yield Curve Models

Affine multiple yield curve models

Derivative Pricing for a Multi-curve Extension of the Gaussian, Exponentially Quadratic Short Rate Model

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