Derivative Pricing under Asymmetric and Imperfect Collateralization and CVA

TL;DR

This paper extends derivative pricing models to account for asymmetric and imperfect collateralization, incorporating credit risk and collateral costs, and provides a practical approximation method for complex pricing formulas.

Contribution

Introduces a unified framework for pricing under asymmetric collateralization using collateral coverage ratio and develops a first-order approximation method.

Findings

Collateral coverage ratio effectively models asymmetric collateralization.

The pricing formula decomposes into market, CVA, and CCA components.

Asymmetric collateralization significantly impacts collateral cost adjustments.

Abstract

The importance of collateralization through the change of funding cost is now well recognized among practitioners. In this article, we have extended the previous studies of collateralized derivative pricing to more generic situation, that is asymmetric and imperfect collateralization with the associated counter party credit risk. By introducing the collateral coverage ratio, our framework can handle these issues in an unified manner. Although the resultant pricing formula becomes non-linear FBSDE and cannot be solve exactly, the fist order approximation is provided using Gateaux derivative. We have shown that it allows us to decompose the price of generic contract into three parts: market benchmark, bilateral credit value adjustment (CVA), and the collateral cost adjustment (CCA) independent from the credit risk. We have studied each term closely, and demonstrated the significant impact of asymmetric collateralization through CCA using the numerical examples.