A Framework for Extracting the Probability of Default from Listed Stock Option Prices
38 Pages Posted: 25 Nov 2011
Date Written: November 14, 2011
This paper develops a framework to estimate the probability of default (PD) implied in listed stock options. The underlying option pricing model measures PD as the intensity of the jump diffusion that the underlying stock price becomes zero. We adopt a two stage calibration algorithm to obtain the precise estimator of PD. In the calibration procedure, we improve the fitness of the option pricing model via the implementation of the time inhomogeneous term structure model in the option pricing model. As the term structure model perfectly fits the actual term structure, we resolve the estimation bias caused by the poor fitness of the time homogeneous term structure model. It is demonstrated that the PD estimator from listed stock options can provide meaningful insights on the pricing of credit derivatives like credit default swap.
Keywords: probability of default (PD), option pricing under credit risk, perturbation method
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