Valuation of Exchange Option with Credit Risk in a Hybrid Model

Geonwoo Kim

doi:10.3390/math8112091

Abstract

In this paper, the valuation of the exchange option with credit risk under a hybrid credit risk model is investigated. In order to build the hybrid model, we consider both the reduced-form model and the structural model. We adopt the probabilistic approach to derive the closed-form formula of an exchange option price with credit risk under the proposed model. Specifically, the change of measure technique is used repeatedly, and the pricing formula is provided as the standard normal cumulative distribution functions.

Highlights

Under the Black–Scholes model [1], Margrabe [2] first derived the closed-form pricing formula of the European exchange option which provides the option holder the right to exchange one risky asset for another
Our main contribution is to propose a hybrid credit risk model and to provide the closed-form pricing formula of vulnerable exchange option under the proposed model based on the probabilistic approach
We propose a valuation of exchange option with credit risk exchange option with credit risk under the hybrid model

Summary

Introduction

Under the Black–Scholes model [1], Margrabe [2] first derived the closed-form pricing formula of the European exchange option which provides the option holder the right to exchange one risky asset for another. 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]. Some researchers considered the generalization of the vulnerable exchange option as a power exchange option They have developed the approaches to price the vulnerable power exchange options under the extensions of the Klein’s credit risk model, such as the jump risk [29,30], the possible default prior to the maturity [31], jumps under the double risk [32] and the intensity based approach [33]. Our main contribution is to propose a hybrid credit risk model and to provide the closed-form pricing formula of vulnerable exchange option under the proposed model based on the probabilistic approach.

The Model

Valuation of the Exchange Option with Credit Risk under the Hybrid Model

Concluding Remarks