Market Models for Credit Risky Portfolios Driven by Time-Inhomogeneous Levy Processes

Eberlein, Ernst; Grbac, Zorana; Schmidt, Thorsten

doi:10.2139/ssrn.2137607

Cited by 2 publications

(7 citation statements)

References 28 publications

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“…The use of time-inhomogeneous Lévy processes in nancial models is justied by their great distributional exibility (cf. Eberlein and Keller [32], Eberlein and Raible [38], Eberlein [29], Eberlein and Kluge [34], Eberlein, Grbac, and Schmidt [42] and Eberlein, Grbac, and Schmidt [41]). …”

Section: Chapter One Mathematical Preliminarymentioning

confidence: 98%

A multiple-curve Lévy forward rate model in a two-price economy

Eberlein

Gerhart

2017

Quantitative Finance

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Abstract. In this thesis, we combine and merge the multiple-curve approach and the two-price theory based on acceptability indices in a Lévy interest rate model.A multiple-curve Heath-Jarrow-Morton (HJM) forward rate model driven by time-inhomogeneous Lévy processes (a multiple-curve Lévy term structure model) is presented. We nd deterministic conditions which ensure the monotonicity of the curves. Explicit valuation formulas for some interest rate derivatives are established, namely forward rate agreements, swaps, caps, oors and digital options. These formulas can numerically be evaluated very fast by using the Fourier based valuation method. Furthermore, we apply the two-price theory to this multiple-curve setting. Ask and bid model prices of caplets, oorlets and digital options are derived.A general procedure how to calibrate this two-price multiple-curve interest rate model to market data is described. As a practical application, the model is calibrated to market prices of caps for dates before and after the global nancial crisis. CONTENTS

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Section: Chapter One Mathematical Preliminarymentioning

confidence: 98%

A multiple-curve Lévy forward rate model in a two-price economy

Eberlein

Gerhart

2017

Quantitative Finance

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“…This assumption imposes unnecessary restrictions to the model, since in practice the set of traded maturities is only finite. The market model approach takes this fact into account, see Eberlein, Grbac, and Schmidt (2012) for a detailed discussion. Here, we follow the framework introduced in this paper with slight modifications.…”

Section: Basic Notionsmentioning

confidence: 99%

“…Remark 3.2. This approach is similar in spirit to Eberlein, Grbac, and Schmidt (2012). However, note that in that paper the forward spreads are modeled, whereas here we decide to model directly the (T k , x)-forward prices which simplifies calibration of the model.…”

Section: Basic Notionsmentioning

confidence: 99%

“…In this article we develop a dynamic market model in the top-down setting, similar in spirit to Eberlein, Grbac, and Schmidt (2012). As discussed in that paper, the market model framework has a number of advantages in comparison to the HJM approaches for credit portfolio modeling.…”

Section: Introductionmentioning

confidence: 99%

“…Taking into account only the traded maturities, one gains an additional degree of freedom in the specification of arbitrage-free models. For example, this allows various additional types of contagion as shown in Eberlein, Grbac, and Schmidt (2012). As a consequence, a tractable affine specification of our model which includes contagion can be obtained.…”

Section: Introductionmentioning

confidence: 99%

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Pricing and Calibration in Market Models

Gehmlich

Grbac

Schmidt

2013

Credit Securitizations and Derivatives

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The goal of this article is to study in detail the pricing and calibration in market models for credit portfolios. Starting from the framework of market models driven by time-inhomogeneous Lévy processes in a top-down approach proposed in Eberlein, Grbac, and Schmidt (2012) we consider a slightly simplified setup which eases calibration. This leads to a new class of affine models which are highly tractable. Conditions for absence of arbitrage under various types of contagion are given and valuation formulas for single tranche CDOs and options on CDO spreads are obtained. A simple two-factor affine diffusion model is calibrated to iTraxx data using the EM-algorithm together with an extended Kalman filter. The model shows a very good fit to all tranches and all maturities over the full observation period of four years.

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Market Models for Credit Risky Portfolios Driven by Time-Inhomogeneous Levy Processes

Cited by 2 publications

References 28 publications

A multiple-curve Lévy forward rate model in a two-price economy

A multiple-curve Lévy forward rate model in a two-price economy

Pricing and Calibration in Market Models

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