Pricing and Calibration in Market Models

Gehmlich, Frank; Grbac, Zorana; Schmidt, Thorsten

doi:10.1002/9781118818503.ch13

Cited by 3 publications

(2 citation statements)

References 25 publications

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“…Note that with H also F is affine. Moreover, as A and B are piecewise constant, the terms α and β are straightforward to compute, see Gehmlich, Grbac, and Schmidt (2013) for detailed computations. The measurement error consists of independent and normally distributed random variables, where the variance of the measurement errors may differ across the observed tranches: ε(k, τ, j + 1) ∼ N (0, σ j+1 ).…”

Section: Calibrationmentioning

confidence: 99%

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Discrete Tenor Models for Credit Risky Portfolios Driven by Time-Inhomogeneous Lévy Processes

Eberlein¹,

Grbac

Schmidt

2013

SIAM J. Finan. Math.

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The goal of this paper is to specify dynamic term structure models with discrete tenor structure for credit portfolios in a top-down setting driven by time-inhomogeneous Lévy processes. We provide a new framework, conditions for absence of arbitrage, explicit examples, an affine setup which includes contagion, and pricing formulas for single tranche collateralized debt obligations (STCDOs) and options on STCDOs. A calibration to iTraxx data with an extended Kalman filter shows an excellent fit over the full observation period. The calibration is done on a set of CDO tranche spreads ranging across six tranches and three maturities. Introduction.Contrary to the single-obligor credit risk models, portfolio credit risk models consider a pool of credits consisting of different obligors and the adequate quantification of risk for the whole portfolio becomes a challenge. A good model for portfolio credit risk should incorporate two components: default risk, which includes, in particular, the dependence structure in the portfolio (also termed default correlation), and spread risk, which represents the risk related to changes of interest rates and changes in the credit quality of the obligors.The main application of such a portfolio model, which we discuss in section 8, is the valuation of tranches of collateralized debt obligations (CDOs) and related derivatives. We would like to emphasize that variants of this model can be used for the valuation of other asset-backed securities. Currently, due to the sovereign credit crisis that has affected Europe, the issuance of so-called European safe bonds (ESBs) is discussed, where the underlying portfolio would consist of sovereign bonds of EU member states with fixed weights set by a strict rule which is proportional to GDP. Our model is easily adapted for pricing of such and other similar asset-backed securities whatever the precise specification of these instruments would be.

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Section: Calibrationmentioning

confidence: 99%

“…This enables us to apply the extended Kalman filter algorithm to obtain a calibration to the full data set. The details of this approach and the extension to more factors can be found in Gehmlich, Grbac, and Schmidt (2013).…”

Section: Calibrationmentioning

confidence: 99%

Discrete Tenor Models for Credit Risky Portfolios Driven by Time-Inhomogeneous Lévy Processes

Eberlein¹,

Grbac

Schmidt

2013

SIAM J. Finan. Math.

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Optimal Cross-Currency Mortgage Decisions

Lütkebohmert

Schmidt

Zhu

2022

Int. J. Theor. Appl. Finan.

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In this paper, we study optimal mortgage decisions in a cross-currency setting. In particular, we address the question on how a household should optimally split its mortgage portfolio in a fixed rate mortgage in the domestic currency and an adjustable rate mortgage denominated in a foreign currency subject to some risk constraints. We propose an affine factor model which allows to jointly investigate the impact of variations in interest rates as well as of exchange rate fluctuations on mortgage decisions. As a case study, we apply our model to real data on Swiss and German mortgage markets and we estimate parameters using a quasi-Kalman filter approach. We then study the impact of different income splits, risk attitudes, and mortgage specifications on the household’s portfolio choice in a mean–variance optimization approach.

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