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(+\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  .
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(+\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 non-linear discounting presented here has several effects, which are relevant in various applications: * If we consider the question of default-free valuation, i.e., factoring in the cost of default protection, the framework can will lead to over-proportional higher values (or cost) for large projects (or damages). The framework can lead to the effect that discount-factors for very large liquidity requirements or projects are an increasing function of time . It may even lead to discount factors larger than one. This may have relevance in the assessment of event like climate change. * For the valuation of defaultable products, e.g., like a defaultable swap, the framework leads to the generation of a continuum of (defaultable) par rate curves (interest rate curve) and the valuation of a payer and a receiver swap differs by more than just a sign .
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framework can lead to
non-linear discounting presented here has several effects, which are relevant in various applications: * If we consider the question of default-free valuation, i.e., factoring in the cost of default protection, the framework can will lead to over-proportional higher values (or cost) for large projects (or damages). The framework can lead to
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. It may even lead to discount factors larger than one. This may have relevance in the assessment of event like climate change. * For the valuation of defaultable products, e.g., like a defaultable swap, the framework leads to the generation of a continuum of (defaultable) par rate curves (interest rate curve) and the valuation of a payer and a receiver swap differs by more than just a sign