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>

Valuation of Commodity-Linked Bond with Stochastic Convenience Yield, Stochastic Volatility, and Credit Risk in an Intensity-Based Model

“…where T is the maturity. Following the works of Wang [23,24], we assume that the intensity process is given by…”

“…We first consider the financial derivative with credit risk. If the payoff function of the derivative is h(S(T)), as in Fard [20] and Wang [23,24], the value of the derivative with credit risk at time 0 in the intensity-based model is given by B = E P we −rτ 1 {0<τ≤T} E P e −r(T−τ) h(S(T))|F (τ) + e −rT E P h(S(T))1 {τ>T}…”

“…Wang [22] considered an intensity-based model based on for valuing vulnerable options in discrete time-a Generalized Autoregressive Conditional Heteroscedasticity (GARCH) process. Furthermore, Wang [23,24] improved the studies for vulnerable option pricing models in intensity-based models by employing a stochastic volatility model and a nonnegative intensity process with two components (systematic risk and idiosyncratic risk). In this study, we investigate the financial derivative with credit risk based on an intensity-based model.…”