Computational methods for default timing
- In risk management and derivatives pricing applications, one frequently works with a reduced-form model of correlated name-by-name default timing. In these models, a name defaults with some conditional default rate, an intensity. We develop, analyze and test transform, Monte Carlo and importance sampling methods for computing a variety of default timing problems. Transform methods are shown to yield (semi-)analytical formulae for various quantities of interest. Existing Monte Carlo simulation methods for default timing problems are surveyed. We introduce a novel concept of a simulation measure to provide a systematic approach to the efficiency and error analysis of these methods. A new Monte Carlo simulation algorithm is then devised to remove a significant source of bias inherent in existing techniques. The setting of rare-event simulation, which falls outside the scope of transform and plain Monte Carlo methods, is also addressed. A new importance sampling estimator which is applicable to any default timing model is proposed. Technical conditions guaranteeing the asymptotic optimality of the resulting estimator are studied in depth. Numerical results illustrate the performance of the estimator in a setting of a complex, portfolio credit risk application.
|Type of resource
|electronic; electronic resource; remote
|1 online resource.
|Shkolnik, Alexander D
|Stanford University, Institute for Computational and Mathematical Engineering.
|Owen, Art B
|Owen, Art B
|Statement of responsibility
|Alexander D. Shkolnik.
|Submitted to the Institute for Computational and Mathematical Engineering.
|Thesis (Ph.D.)--Stanford University, 2014.
- © 2014 by Alexander Dmitri Shkolnik
- This work is licensed under a Creative Commons Attribution Non Commercial 3.0 Unported license (CC BY-NC).
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