Novel Analytic Approach Speeds Calculation of ‘Cheapest-to-Deliver’ Curves for Multi-Currency Collateral
Researchers have developed a faster and more accurate method for calculating “cheapest-to-deliver” discount curves, essential for pricing derivatives subject to multi-currency collateral agreements. The new approach, detailed in a recent paper, addresses a long-standing challenge in financial modeling and aims to improve efficiency in collateralized pricing.
The require for accurate collateral pricing intensified following the 2008 financial crisis, prompting a renewed focus on managing risk associated with multi-currency collateral. When a collateral agreement allows cash to be posted in multiple currencies, determining the cheapest currency to deliver requires discounting with a specialized curve that accounts for the optionality inherent in the choice. Traditionally, these curves have been computed using Monte Carlo simulations, a process that can be computationally intensive.
The research proposes an analytical approximation that leverages established mathematical tools, including the Clark algorithm for maxima of normal variables and Gauss-Hermite quadrature. These tools, combined with optimized discretization and factor-reduction techniques, result in a method that is not only faster but as well more scalable to a larger number of currencies. According to the paper, the approach has been validated through extensive testing across realistic market scenarios.
The “cheapest-to-deliver” currency is determined by identifying the currency that, when posted as collateral, results in the highest equivalent synthetic USD rate. This calculation involves considering the overnight index swap (OIS) rates in each currency and adjusting them using cross-currency basis swaps. The optionality arises from the potential to switch between currencies at any future point in time, making the basis swap volatility a key factor in the calculation, as explained on Quantitative Finance Stack Exchange.
The development of more efficient methods for calculating these curves is crucial for financial institutions managing complex derivative portfolios with multi-currency collateral arrangements. Whereas Monte Carlo simulations offer a high degree of accuracy, the analytical approximation provides a viable alternative for situations where speed and scalability are paramount.
