Pricing vulnerable fader options under stochastic volatility models

Abstract

<p style='text-indent:20px;'>In this paper, we incorporate default risk into Heston's stochastic volatility model and focus on the valuation of vulnerable fader options. Fader options are path-dependent derivatives, depending on the time the underlying asset price stays inside a given range. We obtain an explicit pricing formula of vulnerable fader options, including fader options and (vulnerable) European options as special cases. Finally, we illustrate the effect of stochastic volatility and default risk on fader option prices. Specially, an inverted U-shaped curve is observed when we keep initial levels of the default intensity constant, but change the relative proportions of two factors in the default intensity.</p>