A general first-passage-time model for multivariate credit spreads and a note on barrier option pricing
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2007Author
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http://dx.doi.org/10.22029/jlupub-9564Abstract
We introduce a general continuous stochastic time-change model on Brownian motion in a first-passage-time setting and derive analytical formulas for the first-passage-time distribution in one and several dimensions. Thereby the multi-dimensional model introduces a dependence structure via the time transformation. The two-dimensional model allows, ... in addition, for correlation between the Brownian motions. The model is an extension of the classic Merton model and of the deterministic time-change model by Overbeck and Schmidt. The model is applied to derive an explicit formula for credit-spread and corresponding credit-spread dynamics, especially for the credit-spread volatility. The model can also be used across other assets. In the last chapter we give a note on barrier option pricing.
Wir führen ein allgemeines Erstaustrittszeit Modell ein, welches durch eine stetige stochastische zeittransformierte Brownsche Bewegung gegeben ist. Unter dem eindimensionalen Modell sowie unter dem mehrdimensionalen Modell, welches eine Abhängigkeitsstruktur gegeben durch die Zeittransformation besitzt, bestimmen wir geschlossene Formeln für die ... Verteilung der Erstaustrittszeit. Das Modell ist eine Erweiterung des klassischen Merton Modells und ebenso des Modells von Overbeck und Schmidt, welches eine deterministische Zeittransformation benutzt. Unser Anwendungsschwerpunkt liegt auf dem Modellieren von Credit Spreads und der zugehörigen Credit Spread Dynamik. Mit unserem Modell erhalten wir explizite Formeln für Credit Spread, dessen Dynamik und insbesondere für die Credit Spread Volatilität. Unser Modell kann ebenso auf andere Assetklassen angewendet werden. Wir zeigen dies im letzten Kapitel, in dem wir Barrier Optionen bewerten.
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