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A Unified Framework for Pricing Credit and Equity Derivatives

25 Pages Posted: 20 May 2011  

Erhan Bayraktar

University of Michigan at Ann Arbor - Department of Mathematics

Bo Yang

Morgan Stanley

Date Written: July 2011

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., which only accounts for stochastic volatility.

Keywords: defaultable bond, defaultable stock, equity options, stochastic interest rate, implied volatility, multiscale perturbation method

Suggested Citation

Bayraktar, Erhan and Yang, Bo, A Unified Framework for Pricing Credit and Equity Derivatives (July 2011). Mathematical Finance, Vol. 21, Issue 3, pp. 493-517, 2011. Available at SSRN: https://ssrn.com/abstract=1841232 or http://dx.doi.org/10.1111/j.1467-9965.2010.00435.x

Erhan Bayraktar (Contact Author)

University of Michigan at Ann Arbor - Department of Mathematics ( email )

2074 East Hall
530 Church Street
Ann Arbor, MI 48109-1043
United States

Bo Yang

Morgan Stanley

1585 Broadway
New York, NY 10036
United States

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