  This paper studies the valuation of a class of default swaps with the
embedded option to switch to a different premium and notional principal anytime
prior to a credit event. These are early exercisable contracts that give the
protection buyer or seller the right to step-up, step-down, or cancel the swap
position. The pricing problem is formulated under a structural credit risk
model based on Levy processes. This leads to the analytic and numerical studies
of several optimal stopping problems subject to early termination due to
default. In a general spectrally negative Levy model, we rigorously derive the
optimal exercise strategy. This allows for instant computation of the credit
spread under various specifications. Numerical examples are provided to examine
the impacts of default risk and contractual features on the credit spread and
exercise strategy.
