Pricing of Mexican Interest Rate Swaps in Presence of Multiple Collateral Currencies

TL;DR

This paper develops a post-crisis model for pricing Mexican interest rate swaps considering multiple collateral currencies, including USD, EUR, and MXN, and examines the impact of collateralization and cross-currency swaps.

Contribution

It extends existing models to incorporate multiple collateral currencies and collateralization effects in the Mexican swap market post-2008 crisis.

Findings

Built discounting and projection curves for MXN derivatives with USD, EUR, and MXN collateral

Analyzed pricing differences between collateralized and uncollateralized derivatives

Showed the impact of cross-currency swaps on valuation across collateral currencies

Abstract

The financial crisis of 2007/08 caused catastrophic consequences and brought a bunch of changes around the world. Interest rates that were known to follow or behave similarly of each other diverged. Furthermore, the regulation and in particular the counterparty credit risk began to to be considered and quantified. Consequently, pre-crisis models are no longer valid. Indeed, this work sets the basis to define a valid model that considers the post-crisis world assumptions for the Mexican swap market. The model used in this work was the proposed by Fujii, Shimada and Takahashi in [Fujii et. al., 2010b]. This model allow us to value interest rate derivatives and future cash flows with the existence of a collateral agreement (with a collateral currency). In this document we build the discounting and projection curves for MXN interest rate derivatives considering the collateral currencies: USD, EUR and MXN. Also, we present the pricing when the derivative is uncollateralized. Finally, we show the effect of the cross-currency swaps when valuing through different collateral currencies.