Bilateral Credit Valuation Adjustment of an Optional Early Termination Clause

TL;DR

This paper investigates the valuation of early termination options in swaps considering counterparty risk, deriving a formula that shows such options can significantly affect fair value at inception.

Contribution

It introduces a general pricing formula for bilateral CVA of early termination clauses in uncollateralised swaps with counterparty risk.

Findings

Early termination options can have a non-negligible impact on fair value.

The derived formula accounts for bilateral counterparty risk and optionality.

Impact depends on the timing and risk parameters.

Abstract

Is an option to early terminate a swap at its market value worth zero? At first sight it is, but in presence of counterparty risk it depends on the criteria used to determine such market value. In case of a single uncollateralised swap transaction under ISDA between two defaultable counterparties, the additional unilateral option to early terminate the swap at predefined dates requires a Bermudan credit valuation adjustment. We give a general pricing formula assuming a default-free close-out amount, and apply it in a simplified setting with deterministic intensity and one single date of optional early termination, showing that the impact on the fair value of the transaction at inception might be non negligible.