Pricing vulnerable options in a hybrid credit risk model driven by Heston–Nandi GARCH processes

Abstract

This paper proposes a hybrid credit risk model, in closed form, to price vulnerable options with stochastic volatility. The distinctive features of the model are threefold. First, both the underlying and the option issuer's assets follow the Heston-Nandi GARCH model with their conditional variance being readily estimated and implemented solely on the basis of the observable prices in the market. Second, the model incorporates both idiosyncratic and systematic risks into the asset dynamics of the underlying and the option issuer, as well as the intensity process. Finally, the explicit pricing formula of vulnerable options enables us to undertake the comparative statistics analysis.

Power Exchange Option with a Hybrid Credit Risk under Jump-Diffusion Model

“…Recently, hybrid credit risk models that combine the structural model and reducedform model were proposed to develop the credit risk models for vulnerable options [18][19][20]. The hybrid model is more realistic because it reflects the characteristics of both models.…”

Valuation of Exchange Option with Credit Risk in a Hybrid Model

“…Furthermore, many researchers have studied vulnerable exotic options such as the American option [22], the Asian option [23], the exchange option [24], and the path-dependent option [25] under the structural model. Recently, several researchers proposed the hybrid credit risk models, incorporating the structural model and reduced-form model and provided the pricing formula of vulnerable European option [26,27]. In this paper, we deal with the option valuation based on a hybrid credit risk model.…”