Pricing vulnerable American put options under jump-diffusion processes when corporate liabilities are random

Abstract

This paper develops a valuation model of vulnerable American put options incorporating the correlated credit risk. The dynamics of the underlying asset, the counterparty assets and corporate liabilities are modeled as jump-diffusion processes. The sudden shocks on two related assets and corporate liabilities are divided into systematic component affecting the prices of all assets and idiosyncratic component for each asset. By employing the two-point Geske-Johnson method, we propose an approximate analytical pricing formula for vulnerable American put options. Finally the numerical analysis illustrates the impacts of jump risk and stochastic corporate liabilities on the option prices.

Keywords:

• Multi-exercisable option
• Jump-diffusion
• Random liability
• Vulnerable American option

Acknowledgments

The authors would like to express their deep gratitude to the referee for his/her carefully reading and invaluable comments. The work of Qing Zhou is supported by the National Natural Science Foundation of China (Nos. 11871010 and 11971040) and the Fundamental Research Funds for the Central Universities (No. 2019XD-A11). The work of Weilin Xiao is supported by the National Natural Science Foundation of China (No. 71871202).

Disclosure statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Additional information

Funding

This document is the results of the research project funded by the National Natural Science Foundation of China (Nos. 11871010, 11971040, 71871202), and the Fundamental Research Funds for the Central Universities (No. 2019XD-A11).