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

TL;DR

This paper introduces a closed-form hybrid credit risk model using Heston-Nandi GARCH processes to price vulnerable options, capturing stochastic volatility and both idiosyncratic and systematic risks for more accurate valuation.

Contribution

The paper develops a novel closed-form pricing model for vulnerable options that incorporates stochastic volatility and comprehensive risk factors using Heston-Nandi GARCH processes.

Findings

Model provides explicit pricing formulas for vulnerable options.

Incorporates both idiosyncratic and systematic risks.

Enables comparative statistical analysis of option prices.

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.