General Quadratic Term Structures for Bond, Futures, and Forward Prices

Gaspar, Raquel M.

doi:10.2139/ssrn.913460

Cited by 17 publications

(17 citation statements)

References 21 publications

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“…in El Karoui et al [12], Pelsser [29], Gombani and Runggaldier [17], Leippold and Wu [24], Chen et al [5], and Gaspar [16]. However, since the pre-crisis exponentially affine models are more common, there have also been more attempts to extend them to a post-crisis multi-curve setting (for an overview and details see e.g.…”

Section: The Modelmentioning

confidence: 99%

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: The Modelmentioning

confidence: 99%

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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“…In [14] and [8] it is was shown that the so-called linearquadratic jump-diffusion (LQJD) models are equivalent to the AJD models with an augmented state vector.…”

Section: Extension Of Stochastic Volatility Equity Modelsmentioning

confidence: 99%

Extension of stochastic volatility equity models with the Hull–White interest rate process

Grzelak

Oosterlee

Weeren³

2012

Quantitative Finance

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We present an extension of the stochastic volatility equity models by a stochastic HullWhite interest rate component. We place this system of stochastic differential equations in the class of affine jump diffusion -linear quadratic jump-diffusion processes (Duffie, Pan and Singleton [11], Cheng and Scaillet [8]) so that the pricing of European products can be efficiently done within the Fourier cosine expansion pricing framework [12]. We also apply the model to price some hybrid structured derivatives, which combine the different asset classes: equity and interest rate.

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“…For the risk-free bond market we use the general quadratic term structures setup studied in Gaspar (2004). Consider a finite set of time-dependent factors described by a R m -valued stochastic process (Z t ) t≥0 .…”

Section: Risk-free Bond Marketmentioning

confidence: 99%

“…Moreover, Q(t) is assumed to be symmetric 2 for all t. Gaspar (2004) has shown how to identify these factors a priori from their impact on the drift α, volatility σ or the functional form of the short rate. We, thus, classify the components of Z in the following two groups.…”

Section: W T T≥0mentioning

confidence: 99%

“…Exceptions are Gaspar (2004) and Chen, Filipović, and Poor (2004). Gaspar (2004) introduces the so-called General Quadratic term structure (GQTS) models, which through an a-priori classification of factors include both the affine term structure (ATS) models and the Gaussian-QTS models as special cases. Instead, Chen, Filipović, and Poor (2004) study the traditional Gaussian-QTS, also in for both risk-free and defaultable bonds.…”

Section: Introductionmentioning

confidence: 99%

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Quadratic Models for Portfolio Credit Risk with Shot-Noise Effects

Gaspar

Schmidt

2005

SSRN Journal

Self Cite

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Standard-Nutzungsbedingungen:Die Dokumente auf EconStor dürfen zu eigenen wissenschaftlichen Zwecken und zum Privatgebrauch gespeichert und kopiert werden.Sie dürfen die Dokumente nicht für öffentliche oder kommerzielle Zwecke vervielfältigen, öffentlich ausstellen, öffentlich zugänglich machen, vertreiben oder anderweitig nutzen.Sofern die Verfasser die Dokumente unter Open-Content-Lizenzen (insbesondere CC-Lizenzen) zur Verfügung gestellt haben sollten, gelten abweichend von diesen Nutzungsbedingungen die in der dort genannten Lizenz gewährten Nutzungsrechte. Terms of use: Documents in AbstractWe propose a reduced form model for default that allows us to derive closed-form solutions to all the key ingredients in credit risk modeling: risk-free bond prices, defaultable bond prices (with and without stochastic recovery) and probabilities of survival. We show that all these quantities can be represented in general exponential quadratic forms, despite the fact that the intensity is allowed to jump producing shot-noise effects. In addition, we show how to price defaultable digital puts, CDSs and options on defaultable bonds.Further on, we study a model for portfolio credit risk where we consider both firm specific and systematic risks. The model generalizes the attempt from Duffie and Gârleanu (2001). We find that the model produces realistic default correlation and clustering of defaults. Then, we show how to price first-to-default swaps, CDOs, and draw the link to currently proposed credit indices.

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General Quadratic Term Structures for Bond, Futures, and Forward Prices

Cited by 17 publications

References 21 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

Extension of stochastic volatility equity models with the Hull–White interest rate process

Quadratic Models for Portfolio Credit Risk with Shot-Noise Effects

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