A general HJM framework for multiple yield curve modelling

Cuchiero, Christa; Fontana, Claudio; Gnoatto, Alessandro

doi:10.1007/s00780-016-0291-5

Cited by 63 publications

(35 citation statements)

References 47 publications

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“…One possibility is to extend the market by introducing instruments which are by definition fully collateralized, i.e. natively collateralized assets such as OIS bonds and (textbook) FRAs as in Cuchiero et al (2016) and Cuchiero et al (2019). The resulting model would allow for the joint evolution of interbank spreads, overnight rates, foreign exchange and risky assets.…”

Section: Diffusion Modelsmentioning

confidence: 99%

“…Several spreads have emerged (more precisely widened) between certain interest rates (notably between overnight and unsecured Ibor rates) and these rates in turn differ from interest rates agreed in the context of repurchase agreements (repo rates). From a modeling perspective this resulted in the development of multi curve interest rate models as in Henrard (2007), Bianchetti (2010), Moreni and Pallavicini (2014), Mercurio (2010), Henrard (2014), Grbac et al (2015), Crépey et al (2015) Cuchiero et al (2016) and Cuchiero et al (2019) among others.…”

Section: Introductionmentioning

confidence: 99%

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Cross Currency Valuation and Hedging in the Multiple Curve Framework

Gnoatto

Seiffert²

2020

SSRN Journal

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We generalize the results of Bielecki and Rutkowski (2015) on funding and collateralization to a multi-currency framework and link their results with those of Piterbarg (2012), Pallavicini (2017), andFujii et al. (2010b).In doing this, we provide a complete study of absence of arbitrage in a multi-currency market where, in each single monetary area, multiple interest rates coexist. We first characterize absence of arbitrage in the case without collateral.After that we study collateralization schemes in a very general situation: the cash flows of the contingent claim and those associated to the collateral agreement can be specified in any currency. We study both segregation and rehypothecation and allow for cash and risky collateral in arbitrary currency specifications. Absence of arbitrage and pricing in the presence of collateral are discussed under all possible combinations of conventions.Our work provides a reference for the analysis of wealth dynamics, we also provide valuation formulas that are a useful foundation for cross-currency curve construction techniques. Our framework provides also a solid foundation for the construction of multi-currency simulation models for the generation of exposure profiles in the context of xVA calculations.2010 Mathematics Subject Classification. 91G30, 91B24, 91B70. JEL Classification E43, G12.

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Section: Diffusion Modelsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Cross Currency Valuation and Hedging in the Multiple Curve Framework

Gnoatto

Seiffert²

2020

SSRN Journal

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“…However, more recent studies show that these spreads have actually become quite substantial since the latest financial crisis (see, e.g. , Cuchiero et al 2016, Grasselli and Miglietta 2016. This evidence suggests that future cash flows should no longer be discounted and generated by the same yield curve, but by different curves (Kijima et al 2009).…”

Section: Introductionmentioning

confidence: 99%

Stochastic interest rate modelling using a single or multiple curves: an empirical performance analysis of the Lévy forward price model

Verschuren

2020

Quantitative Finance

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In current financial markets negative interest rates have become rather persistent, while in theory it is often common practice to discard such rates as incredible and irrelevant. However, from a risk management perspective, it is crucially important to financial institutions to properly account for this phenomenon in their Asset Liability Management (ALM) studies. In this paper, we develop a coherent framework on how to best incorporate negative interest rates in these studies through a single curve stochastic term structure model and compare it to its multiple curve analogue. It turns out that, from the wide range of available single curve models, especially the Lévy Forward Price model (LFPM) of Eberlein and Özkan [The Lévy LIBOR model. Financ. Stoch., 2005, 9, 327-348] seems appropriate for ALM purposes. This paper describes an optimisation routine for calibrating this LFPM under the risk-neutral measure in both the single and multiple curve framework to the market prices of interest rate caplets with different strike rates, maturities and tenors. In addition, an empirical performance analysis is made of the single and multiple curve LFPM, where we include four deterministic volatility specifications and provide an explicit parametrisation of a piecewise homogeneity restriction with both deterministic and random breakpoints. This comparative analysis indicates that both the single and multiple curve LFPM is best adopted with the Linear-Exponential Volatility (LEV) specification and that deterministic breakpoints should be included, rather than random breakpoints.

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“…Kijima et al (2009), apply the methodology to study two short rate models, the Vasicek model and the quadratic Gaussian model, and use them for the valuation of bond options and swaptions. Mercurio (2009Mercurio ( , 2010 and Grbac et al (2015) extend the libor market model (LMM) to be compatible with the multi-curve practice and price caplets and swaptions, while more recently, Pallavicini and Tarenghi (2010), Crépey et al (2012), Moreni and Pallavicini (2014) and Cuchiero et al (2016) extend the classical HeathJarrow-Morton (HJM) framework to incorporate multiple curves in order to price interest rate products such as forward starting interest rate swaps (IRS), plain vanilla European swaptions and CMS spread options. Finally, important contributions include Crépey et al (2015) who develop a Levy-based HJM model for credit value adjustment (CVA) and Fanelli (2016) who develop a defaultable HJM model for pricing basis swaps in a multi-curve setup.…”

Section: Introductionmentioning

confidence: 99%

Convexity adjustment for constant maturity swaps in a multi-curve framework

2017

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In this paper we propose a double curving setup with distinct forward and discount curves to price constant maturity swaps (CMS). Using separate curves for discounting and forwarding, we develop a new convexity adjustment, by departing from the restrictive assumption of a flat term structure, and expand our setting to incorporate the more realistic and even challenging case of term structure tilts. We calibrate CMS spreads to market data and numerically compare our adjustments against the Black and SABR (stochastic alpha beta rho) CMS adjustments widely used in the market. Our analysis suggests that the proposed convexity adjustment is significantly larger compared to the Black and SABR adjustments and offers a consistent and robust valuation of CMS spreads across different market conditions.

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A general HJM framework for multiple yield curve modelling

Cited by 63 publications

References 47 publications

Cross Currency Valuation and Hedging in the Multiple Curve Framework

Cross Currency Valuation and Hedging in the Multiple Curve Framework

Stochastic interest rate modelling using a single or multiple curves: an empirical performance analysis of the Lévy forward price model

Convexity adjustment for constant maturity swaps in a multi-curve framework

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