Debt Write-Off

When a credit line becomes delinquent, its market value should reflect both the probability of loss and the probability of recovery. Instead of an immediate full markdown to zero, we introduce a model which dynamically adjusts the markdown based on the probability-weighted expected recovery. This ensures that the markdown reflects real-world expectations while preserving the option for future recoveries. The total adjusted market value M (t) of a delinquent credit line is given by:

$$L(t) = \frac{1}{1 + e^{-k(t - t_c)}}$$

$$R(t) = \frac{R_{\max}}{1 + e^{k_r(t - t_r)}}$$

$$M(t) = (1 - L(t)) + R(t)$$

$$\text{where } \begin{cases} \begin{aligned} t &= \text{Time in days since delinquency began} \\ t_c &= \text{Half-life (time when the credit line is 50\% marked down)} \\ t_r &= \text{Time threshold beyond which recoveries significantly decline} \\ k &= \text{Steepness of the markdown curve} \\ R_{\max} &= \text{Maximum expected recovery rate} \\ L(t) &= \text{Loss probability markdown} \\ R(t) &= \text{Expected recovery rate} \\ M(t) &= \text{Market value multiplier} \\ \end{aligned} \end{cases}$$

This model ensures an accurate valuation of non-performing credit lines while maintaining protocol solvency and preventing market panic from sudden markdowns to zero. This function ensures that at the early stages of delinquency, recoveries are still probable, reducing the markdown severity. How- ever, as delinquency time increases, the likelihood of successful recovery diminishes. By dynamically adjusting for expected recovery, it provides a more nuanced and realistic approach to loss recognition. Credit lines are preemptively marked down to 0 cents on the dollar upon delinquency status in order to disincentivize runs on the money market.