On the Pricing of Performance Sensitive Debt

Abstract

Performance sensitive debt (PSD) contracts link a loan's interest rate to the borrower's measure of credit relevant firm performance, e.g., if the borrower becomes less creditworthy, the interest rate increases according to a predetermined schedule. PSD provisions are included in approximately 35% of all U.S. and Canadian corporate loans (1994. Based on standard no-arbitrage theory and observed contractual specifications, we derive and empirically test a new pricing model for PSD contracts with a cash flow driven performance measure. Our sample consists of 270 PSD loans where the loan contractual terms are collected from Thomson Reuter's Dealscan database and the borrower information is collected from Compustat and CRSP. The theoretical market value of a PSD contract is on average 3.2% above par value at the time of issue. By considering the subsamples of only interest increasing and interest decreasing PSD contracts, respectively, we find that the former is overpriced by 7.7% on average, whereas the latter, on average, exhibits no significant mispricing. The empirically observed overpricing of interest increasing contracts is consistent with the signalling hypothesis of Manso, Strulovici & Tchistyi (2010) and the cost of moral hazard explanation of Asquith, Beatty & Weber (2005). The not significant mispricing of interest decreasing contracts is consistent with the idea that borrowers have increased bargaining power in the form of outside alternative financing options for these contracts.

The role of asset payouts in the estimation of default barriers

“…2, such task would be time-consuming and would make the empirical validation of the PBT model extremely difficult. Therefore, we approximate P V D as the limit of a finite multi-level annuity with bankruptcy risk, based on the results of Mjøs and Persson (2010) and Mjøs et al (2013). The present value of dividends is treated as a portfolio of primitive Arrow-Debreu securities, whose value is mathematically expressed as…”

“…This improvement generates a full range of reasonable barrier levels in relation to the firmâs liabilities. A new feature in our approach is that we employ the methodology of Mjøs and Persson (2010) and Mjøs et al (2013) to approximate the present value of dividends as the limit of a finite multi-level annuity with bankruptcy risk. Another feature is that our sample includes not only the industrial firms used in the original BT model, but also banks.…”

“…We approximate the claim P V D(H, q) as the limit of a finite multi-level annuity with bankruptcy risk, based on the results of Mjøs and Persson (2010) and Mjøs et al (2013). Let us denote with H i , i ∈ ¶1, 2, ..., n + m♢ a sequence of non-absorbing barriers that are greater than the default barrier H. Given the initial asset value V 0 , we have n non-absorbing barriers that are greater than V 0 , and m that are below V 0 .…”

“…If we denote with P V D(H, q) the approximate present value of dividends described by Eq. 17, then from Mjøs et al (2013) we can derive the following solution…”

“…historical cost accounting), even if the regulator imposes positive minimum capital requirements (Kane, 1989;Harding et al, 2013), and (ii) the regulator follows a capital forbearance policy (Ronn and Verma, 1986). Mjøs et al (2013), since the present value of dividends is approximated as the limit of a finite multi-level annuity with bankruptcy risk, and to the model of Ingersoll (1976) for dual purpose funds which occurs as a special solution when the barrier is zero. The paper is also related to structural model applications in banking (Episcopos, 2008;Harding et al, 2013;Chang, 2014;Leanza et al, 2021), due to the direct influence of the regulators on the default barrier of financial institutions.…”