A Monte Carlo approach to American options pricing including counterparty risk

ABSTRACT

In this work, we propose a numerical technique to compute the total value adjustment for the pricing of American options when considering counterparty risk. Several linear and nonlinear mathematical models, associated to different choices of the mark-to-market value at default, are deduced and numerically solved, thus leading to approximations of the option price with counterparty risk. The methodology is based on Monte Carlo simulations combined with a dynamic programming strategy. At each time step, an optimal stopping criterion is applied and the decision on either exercising or not the option is taken. We present some numerical tests to illustrate the behaviour of the proposed method.

KEYWORDS:

• American options
• counterparty risk
• total value adjustment
• Monte Carlo method
• dynamic programming

2010 MATHEMATICS SUBJECT CLASSIFICATIONS:

• 91G60
• 91G40

Acknowledgements

The authors are very grateful to both reviewers for their valuable comments and suggestions, which contributed to improve the manuscript.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work has been financially supported by the Spanish government (Ministerio de Economía y Competitividad, project MTM2016-76497-R) and Xunta de Galicia (grant number GRC2014/044, including FEDER funds). Second author is partially supported by Spanish Predoc Fellowship [grant number BES-2014-070782].