A multiple-curve HJM model of interbank risk

Crépey, Stéphane; Grbac, Zorana; Nguyen, Hai-Nam

doi:10.1007/s11579-012-0083-4

Cited by 63 publications

(58 citation statements)

References 25 publications

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“…Kijima et al [22], Crépey et al [8], Filipović and Trolle [14]), one possibility is now to keep the classical relationship (6) also for L(T ; T , T + Δ) thereby replacing however the bonds p(t, T ) by fictitious risky onesp(t, T ) that are assumed to be affected by the same factors as the Libor rates. Such a bond can be seen as an average bond issued by a representative bank from the Libor group and it is therefore sometimes referred to in the literature as a Libor bond.…”

Section: Martingale Measuresmentioning

confidence: 99%

“…Note that we shall model the bond pricesp(t, T ), for all t and T with t ≤ T , even though only the pricesp(T , T + Δ), for all T , are needed in relation (8). Moreover, keeping in mind that the bondsp(t, T ) are fictitious, they do not have to satisfy the boundary conditionp(T , T ) = 1, but we still assume this condition in order to simplify the modeling.…”

Section: Martingale Measuresmentioning

confidence: 99%

“…Recalling that for the Libor rate we had postulated the relation (8) to hold at the inception time T , namely…”

Section: Frasmentioning

confidence: 99%

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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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Section: Martingale Measuresmentioning

confidence: 99%

Section: Martingale Measuresmentioning

confidence: 99%

See 1 more Smart Citation

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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“…Through its discounting implications, this systemic component of counterparty risk has impacted all derivative markets. This means that in the current market conditions, one should actually use multiple-curve clean value models of interest rate derivatives in the TVA computations (see for instance [CGN12] and the references therein). In order not to blur the main flow of argument we postpone this to a follow-up work.…”

Section: Clean Valuationsmentioning

confidence: 99%

Counterparty Risk and Funding: The Four Wings of the Tva

Crépey

Gerboud

Grbac

et al. 2013

Int. J. Theor. Appl. Finan.

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The credit crisis and the ongoing European sovereign debt crisis have highlighted the native form of credit risk, namely the counterparty risk. The related Credit Valuation Adjustment (CVA), Debt Valuation Adjustment (DVA), Liquidity Valuation Adjustment (LVA) and Replacement Cost (RC) issues, jointly referred to in this paper as Total Valuation Adjustment (TVA), have been thoroughly investigated in the theoretical papers [Cr12a] and [Cr12b]. The present work provides an executive summary and numerical companion to these papers, through which the TVA pricing problem can be reduced to Markovian pre-default TVA BSDEs. The first step consists in the counterparty clean valuation of a portfolio of contracts, which is the valuation in a hypothetical situation where the two parties would be risk-free and funded at a risk-free rate. In the second step, the TVA is obtained as the value of an option on the counterparty clean value process called Contingent Credit Default Swap (CCDS). Numerical results are presented for interest rate swaps in the Vasicek, as well as in the inverse Gaussian Hull-White short rate model, also allowing one to assess the related model risk issue.

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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 multiple-curve HJM model of interbank risk

Cited by 63 publications

References 25 publications

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

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

Counterparty Risk and Funding: The Four Wings of the Tva

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

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