  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 the model implied credit
default swap (CDS) spread matches the market CDS spread and that our model
produces a very desirable CDS spread term structure. This is observation is
worth noticing since without calibrating any parameter to the CDS spread data,
it is matched by the CDS spread that our model generates using the available
information from the equity options and corporate bond markets. We also observe
that our model matches the equity option implied volatility surface well since
we properly account for the default risk premium 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, Papanicolaou, Sircar and Solna (2003), which only accounts for
stochastic volatility.
