A Unified View of LIBOR Models

Glau, Kathrin; Grbac, Zorana; Papapantoleon, Antonis

doi:10.1007/978-3-319-45875-5_18

Cited by 5 publications

(3 citation statements)

References 31 publications

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“…The definition of multiple curve affine LIBOR models implies that the dynamics of OIS forward rates and forward LIBOR rates, more precisely of 1 + δ x F x k and 1 + δ x L x k , exhibit an exponential-affine dependence in the driving process X; see (3.5) and (3.8). Glau, Grbac, and Papapantoleon (2016) recently showed that models that exhibit this exponential-affine dependence are the only ones that produce structure preserving LI-BOR models; cf. Proposition 3.11 therein.…”

Section: Affine Libor Models With Multiple Curvesmentioning

confidence: 99%

Continuous tenor extension of affine LIBOR models with multiple curves and applications to XVA

Papapantoleon

Wardenga²

2018

Probab Uncertain Quant Risk

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which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. AbstractWe consider the class of affine LIBOR models with multiple curves, which is an analytically tractable class of discrete tenor models that easily accommodates positive or negative interest rates and positive spreads. By introducing an interpolating function, we extend the affine LIBOR models to a continuous tenor and derive expressions for the instantaneous forward rate and the short rate. We show that the continuous tenor model is arbitrage-free, that the analytical tractability is retained under the spot martingale measure, and that under mild conditions an interpolating function can be found such that the extended model fits any initial forward curve. This allows us to compute value adjustments (i.e. XVAs) consistently, by solving the corresponding 'pre-default' BSDE. As an application, we compute the price and value adjustments for a basis swap, and study the model risk associated to different interpolating functions.

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Section: Affine Libor Models With Multiple Curvesmentioning

confidence: 99%

Continuous tenor extension of affine LIBOR models with multiple curves and applications to XVA

Papapantoleon

Wardenga²

2018

Probab Uncertain Quant Risk

Self Cite

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“…The last financial crisis (2007)(2008) has greatly increased the monitoring and pricing of CCR on OTC-markets products and many researchers and practitioners tried to develop a general framework for a better assessment of the CVA evaluation to compensate a derivatives holder for taking CCR. Indeed, along the years, other value adjustments have been additionally considered leading to the acronym (X)VA. An updated overview of the recent research directions under investigation is presented in [15].…”

Section: Introductionmentioning

confidence: 99%

Cva and Vulnerable Options in Stochastic Volatility Models

Alòs

Antonelli

Ramponi

et al. 2021

Int. J. Theor. Appl. Finan.

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This work aims to provide an efficient method to evaluate the Credit Value Adjustment (CVA) for a vulnerable European option, which is an option subject to some default event concerning the issuer solvability. Financial options traded in OTC markets are of this type. In particular, we compute the CVA in some popular stochastic volatility models such as SABR, Hull et al., which have proven to fit quite well market derivatives prices, admitting correlation with the default event. This choice covers the relevant case of Wrong Way Risk (WWR) when a credit deterioration determines an increase in the claim value. Contrary to the structural modeling adopted in [G. Wang, X. Wang & K. Zhu (2017) Pricing vulnerable options with stochastic volatility, Physica A 485, 91–103; C. Ma, S. Yue & Y. Ma (2020) Pricing vulnerable options with Stochastic volatility and Stochastic interest rate, Computational Economics 56, 391–429], we use the reduced-form intensity-based approach to provide an explicit representation formula for the vulnerable option price and related CVA. Later, we specialize the evaluation formula and construct its approximation for the three models mentioned above. Assuming a CIR model for the default intensity process, we run a numerical study to test our approximation, comparing it with Monte Carlo simulations. The results show that for moderate values of the correlation and maturities not exceeding one year, the approximation is very satisfactory as of accuracy and computational time.

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“…Moreover, models based on a forward process are able to better describe market dynamics than market models can, and a driving Lévy process is generally more suitable for capturing market fluctuations than the classical Black-Scholes model (Black and Scholes 1973, Henrard 2005, Hilber et al 2009. More importantly, the LFPM is in fact capable of dealing with negative LIBOR rates (Glau et al 2016).…”

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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A Unified View of LIBOR Models

Cited by 5 publications

References 31 publications

Continuous tenor extension of affine LIBOR models with multiple curves and applications to XVA

Continuous tenor extension of affine LIBOR models with multiple curves and applications to XVA

Cva and Vulnerable Options in Stochastic Volatility Models

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

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