Affine LIBOR Models with Multiple Curves: Theory, Examples and Calibration

Grbac, Zorana; Papapantoleon, Antonis; Schoenmakers, John; Skovmand, David

doi:10.1137/15m1011731

Cited by 50 publications

(64 citation statements)

References 39 publications

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“…In the former case, since the market only provides cap and not caplet volatilities, the calibration routine can be simplified by first bootstrapping a surface of caplet volatilities from the observed surface of cap volatilities, along the lines of [50]. Finally, as we show in [11], the multiple curve extension of affine Libor models proposed by [30] can be regarded as a discrete tenor version of our affine specification, so that the calibration techniques (with respect to caplet data) introduced in that paper can be also employed in our context.…”

Section: General Aspects Of Model Implementation and Calibrationmentioning

confidence: 99%

“…From a modeling perspective, as in the case of classical interest rate models, most of the models proposed so far in the literature can be ascribed to three main mutually related families: short-rate approaches, Libor market models and HJM models. Referring to Section 6 for a detailed comparison of the different approaches, we just mention that multiple curve short rate models have been first introduced in [44], [43], [24] and, more recently, in [56] and [28], while Libor market models have been extended to the multiple curve setting in [51], [52] and, more recently, in [30]. In a related context, [53] propose a model for additive spreads which can be applied on top of any classical single-curve interest rate model.…”

Section: Introductionmentioning

confidence: 99%

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A general HJM framework for multiple yield curve modelling

2016

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Abstract. We propose a general framework for modeling multiple yield curves which have emerged after the last financial crisis. In a general semimartingale setting, we provide an HJM approach to model the term structure of multiplicative spreads between FRA rates and simply compounded OIS risk-free forward rates. We derive an HJM drift and consistency condition ensuring absence of arbitrage and, in addition, we show how to construct models such that multiplicative spreads are greater than one and ordered with respect to the tenor's length. When the driving semimartingale is an affine process, we obtain a flexible and tractable Markovian structure. Finally, we show that the proposed framework allows to unify and extend several recent approaches to multiple yield curve modeling.

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Section: General Aspects Of Model Implementation and Calibrationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A general HJM framework for multiple yield curve modelling

2016

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“…While research on multi-curve interest rates models was and is very active, see, e.g., [5,6,15,[20][21][22], references therein and the other chapters of in this book, the construction of the initial interest rate curve, here f 0 (T ), naturally does not get a similar strong attention. However, a good curve construction is of high importance for practitioners, since it has a strong impact on the delta-hedge (that is, the first-order interest rate risk).…”

Section: Df (T T ) = μ(T T )Dt + σ(T T )Dw (T)mentioning

confidence: 99%

Multi-curve Construction

Fries

2016

Innovations in Derivatives Markets

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In this chapter we discuss the definition, construction, interpolation and application of curves. We will discuss discount curves, a tool for the valuation of deterministic cash-flows and forward curves, a tool for the valuation of linear cashflows of an index. A curve is mainly a tool to interpolate certain basic financial products (zero coupon bonds, FRAs) with respect to maturity date and fixing date, such that it can be used to value products, which can be represented as linear functions of possibly interpolated values of a discount or forward curve. For this, the chosen interpolation method and interpolation entity plays an important role. Distinguishing forward curves from discount curves (representing the collateralization of the forward) motivates an alternative interpolation method, namely interpolation of the forward value (the product of the forward and the discount factor). In addition, treating forward curves as native curves (instead of representing them by pseudodiscount curves) will avoid other problems, like that of overlapping instruments. Besides the interpolation, we discuss the calibration of the curves for which we give a generic object-oriented implementation in Fries (Curve calibration. Object-oriented reference implementation, 2010-2015, [11]). We give some numerical results, which have been obtained using this implementation and conclude with a remark on how to define term-structure models (analog to a LIBOR market model) based on the definition of the performance index of an accrual account associated with a discount curve.

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“…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%

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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Affine LIBOR Models with Multiple Curves: Theory, Examples and Calibration

Cited by 50 publications

References 39 publications

A general HJM framework for multiple yield curve modelling

A general HJM framework for multiple yield curve modelling

Multi-curve Construction

Cross Currency Valuation and Hedging in the Multiple Curve Framework

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