Non-Linear Discounting and Default Compensation: Valuation of Non-Replicable Value and Damage: When the Social Discount Rate may Become Negative

Abstract

In this short note we develop a model for discounting. A focus of the model is the discounting, when discount factors cannot be derived from market products. That is, a risk-neutralizing trading strategy cannot be performed. This is the case, when one is in need of a risk-free (default-free) discounting, but default protection on funding providers is not traded. For this case, we introduce a default compensation factor ($\exp(+\tilde{\lambda} T)$) that describes the present value of a strategy to compensate for default (like buying default protection would do). In a second part, we introduce a model, where the survival probability depends on the required notional. This model is different from the classical modelling of a time-dependent survival probability ($\exp(-\lambda T)$). The model especially allows that large liquidity requirements are instantly more likely do default than small ones. Combined the two approaches build a framework in which discounting (valuation) is non-linear. The framework can lead to the effect that discount-factors for very large liquidity requirements or projects are an increasing function of time.