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.
Highlights
To the best of our knowledge, the first mathematically correct expression for the holder’s once-extendible put option is to be found in Wu [4]; subsequently a more general treatment of single-period extendible puts is given by Shevchenko [2] and the general closed-form solution for n-time extendible options is provided by Chung and Johnson [5]
The first one provides the closed-form solution of the put option embedded in once-extendible credit commitments and the second one determines in a ratings-based model the capital charge corresponding to the credit risk exposure of such commitments
Put valuation taking place at the future date T1 is based on forward risk neutrality with zero-coupon bonds as discount factor
Summary
This paper offers a solution to the following problem: How to account for the creditrisk exposure of extendible loan commitments subject to Basel-3 micro-prudential. O’Hara and Constantinou [13] apply the fast Fourier transform to improve their computational efficiency when the once-extendible options are derived as semi-analytic expressions Regarding their application to credit commitments we found but one reference, Chateau and Wu [14]. In their borrower’s extendible expression, Equation (9), discounting is done over two different periods with a constant risk-free rate of interest. Since extendible commitments are term-wise hybrid instruments, we propose to replace Basel simplified approach by an Advanced Internal-Ratings Based (AIRB) model that allows credit risk to be spread over at least two time periods.
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