Libor model with expiry-wise stochastic volatility and displacement

Ladkau, Marcel; Schoenmakers, John; Zhang, Jianing

doi:10.1504/ijpam.2013.054401

Cited by 3 publications

(5 citation statements)

References 26 publications

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“…However, since interest rate derivative markets remain highly segmented and joint calibration of caplets and swaptions is a perennial challenge, see e.g. Brigo and Mercurio (2006) or Ladkau, Schoenmakers, and Zhang (2013), we will leave this issue for future research. The model construction summarized in has the advantage that caplets can be calibrated sequentially one maturity at a time starting at the longest maturity and then moving backwards.…”

Section: 1mentioning

confidence: 99%

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

Grbac¹,

Papapantoleon²,

Schoenmakers³

et al. 2015

SIAM J. Finan. Math.

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Abstract. We introduce a multiple curve framework that combines tractable dynamics and semi-analytic pricing formulas with positive interest rates and basis spreads. Negatives rates and positive spreads can also be accommodated in this framework. The dynamics of OIS and LIBOR rates are specified following the methodology of the affine LIBOR models and are driven by the wide and flexible class of affine processes. The affine property is preserved under forward measures, which allows us to derive Fourier pricing formulas for caps, swaptions and basis swaptions. A model specification with dependent LIBOR rates is developed, that allows for an efficient and accurate calibration to a system of caplet prices.

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Section: 1mentioning

confidence: 99%

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

Grbac¹,

Papapantoleon²,

Schoenmakers³

et al. 2015

SIAM J. Finan. Math.

Self Cite

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“…Although this pricing procedure is more or less standard, we still present it here for the convenience of the reader (cf. also [14]).…”

Section: Remarkmentioning

confidence: 87%

“…By taking p = d * in the case d ≥ d * and letting F 1 and G 1 be matrices as specified above with F 1 F ⊤ 1 = R * and G 1 G ⊤ 1 = R * , we have that for any |ϱ| ≤ 1, F ϱ = ϱF 1 and G ϱ = √ 1 − ϱ 2 G 1 solve the matrix equation (14). Let us specialize to the case d = d * = p : A matrix G with GG ⊤ = R * is determined up to a orthogonal transformation.…”

Section: A Simple Pragmatic Solutionmentioning

confidence: 99%

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Coupling local currency Libor models to FX Libor models

Schoenmakers

2012

Recent Developments in Computational Finance

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We focus on the coupling of two existing and calibrated single currency Libor models into a joint Libor model that allows for pricing of multiple currency based structured interest rate products. Our main contribution is twofold: On the one hand we provide a method for synthesizing two local currency based correlation structures into a correctly defined joint correlation structure that describes the cross Libor correlations between the two currencies in a realistic way. On the other hand we introduce an (necessary) FX related factor X in order to describe the unified model with respect to one particular numéraire measure. In addition we propose to calibrate this factor to FX instruments in the case where X is modeled via Heston type dynamics.

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“…Additionally, various extensions of the LI-BOR market model to stochastic volatility have also appeared in the literature, cf. Wu and Zhang (2006), Belomestny, Mathew, andSchoenmakers (2009) andLadkau, Schoenmakers, andZhang (2013). Recently, a modeling approach under one single forward measure, the terminal measure, has been proposed in Keller-Ressel, Papapantoleon, and Teichmann (2013), which is based on affine processes.…”

Section: Introductionmentioning

confidence: 99%

A Unified View of LIBOR Models

Glau

Grbac

Papapantoleon

2016

Springer Proceedings in Mathematics &Amp; Statistics

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We provide a unified framework for modeling LIBOR rates using general semimartingales as driving processes and generic functional forms to describe the evolution of the dynamics. We derive sufficient conditions for the model to be arbitrage-free which are easily verifiable, and for the LIBOR rates to be true martingales under the respective forward measures. We discuss when the conditions are also necessary and comment on further desirable properties such as those leading to analytical tractability and positivity of rates. This framework allows to consider several popular models in the literature, such as LIBOR market models driven by Brownian motion or jump processes, the Lévy forward price model as well as the affine LIBOR model, under one umbrella. Moreover, we derive structural results about LIBOR models and show, in particular, that only models where the forward price is an exponentially affine function of the driving process preserve their structure under different forward measures.2010 Mathematics Subject Classification. 91G30, 60G44. Key words and phrases. LIBOR, forward price, semimartingales, LIBOR market models, Lévy forward price models, affine LIBOR models.Financial support from the PROCOPE project "Financial markets in transition: mathematical models and challenges" and the Europlace Institute of Finance project "Post-crisis models for interest rate markets" is gratefully acknowledged.

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Libor model with expiry-wise stochastic volatility and displacement

Cited by 3 publications

References 26 publications

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

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

Coupling local currency Libor models to FX Libor models

A Unified View of LIBOR Models

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