A Unified Framework for Pricing Credit and Equity Derivatives

by Erhan Bayraktar of the University of Michigan, and
Bo Yang of Morgan Stanley

March 2009

Abstract: We propose a model which can be jointly calibrated to the corporate bond term structure and equity option volatility surface of the same company. Our purpose is to obtain explicit bond and equity option pricing formulas that can be calibrated to find a risk neutral model that matches a set of observed market prices. This risk neutral model can then be used to price more exotic, illiquid or over-the-counter derivatives. We observe that our model matches the equity option implied volatility surface well since we properly account for the default risk in the implied volatility surface. We demonstrate the importance of accounting for the default risk and stochastic interest rate in equity option pricing by comparing our results to Fouque et al. (2003), which only accounts for stochastic volatility.

JEL Classification: G13.

Keywords: Defaultable Bond, Defaultable Stock, Equity Options, Stochastic Interest Rate, Implied Volatility, Multiscale Perturbation Method.

Published in: Mathematical Finance, Vol. 21, No. 3, (July 2011), pp. 493-517.

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