Pricing the Credit-Risk Put Embedded in Borrowers’ Extendible Credit Commitments, with Its Application to Basel-3 Micro-Prudential Regulation

Abstract

This research makes two contributions: 1) use a term structure framework to price analytically the put option implicit in borrowers’ extendible credit commitments and 2) use the latter to compute in a ratings-based model the capital charge corresponding to the credit-risk exposure of such commitments. Since the term structure of interest rates is stochastic, the zero-coupon bonds in the put closed-form solution delink discounting factor from the credit and funding rates that define the credit spread appearing in the put payoff. By essence, extendible commitments straddle the term-based commitment classification of Basel-3 simplified approach. To improve this, we formulate a ratings-based model that combines extendible put values with new coefficients (forward funding proportion and exposure at funding) as well as a matrix that captures credit-ratings migration over time. Moreover, the combination is versatile enough to deal with a borrower’s credit downgrade and its attendant incremental Basel-3 capital charge.