论文标题
非线性折现和默认补偿：不可再生价值和损害的估值：当社会折现率可能变为负数时
Non-Linear Discounting and Default Compensation: Valuation of Non-Replicable Value and Damage: When the Social Discount Rate may become Negative
论文作者
论文摘要
在本文中，我们介绍了一个模型，该模型增加了折扣的非线性：折现因子可能取决于名义（即，折扣值在名义中不再是线性的）。在本文的第一部分中，当无法从市场产品中得出折扣因素时，我们会提供折扣。也就是说，不能执行一种中和交易策略。当一个人需要无风险（默认的）折扣时，情况就是这种情况，但是对资金提供商的默认保护没有交易。在这种情况下，我们得出了一个默认补偿因子，该因素描述了赔偿违约策略的现值（例如购买默认保护措施）。在本文的第二部分中，我们介绍了一个模型，其中生存概率及其折现因子取决于名义。该模型引入了与时间有关的生存概率的经典建模中不存在的效果。我们的模型允许与小型流动性要求更可能立即默认。结合在一起，这两种型号构建了一个框架，其中折现（因此估值）是非线性的：折现因素取决于要打折的金额。 我们的方法基于经典的折现理论（可以作为市场涂抹或源自效用，消费和生产的模型）。从这个意义上讲，它是一种概括而不是替代方案。模型方法与气候模型具有特定的相关性，在评估未来事件的严重性方面，折现是一个重要方面。我们的模型可能会导致某些情况下未偿还的折现因子（负折现率）。
In this paper, we introduce a model that adds a non-linearity to discounting: the discounting factor may depend on the notional (i.e., discounted values are no longer linear in the notional). In the first part of the paper, we provide a discounting when discount factors cannot be derived from market products. That is, a risk-neutralising trading strategy cannot be performed. This is the case when one needs a risk-free (default-free) discounting, but default protection on funding providers is not traded. For this case, we derive a default compensation factor that describes the present value of a strategy to compensate for default (like buying default protection would do). In a second part of the paper, we introduce a model where the survival probability, and hence the discount factor, depends on the notional. This model introduces an effect not present in the classical modelling of a time-dependent survival probability. Our model allows that large liquidity requirements are more likely to default instantly than small ones. Combined, the two models build a framework where discounting (and hence valuation) is non-linear: discount factors depend on the amount to be discounted. Our approach builds on top of the classical theory of discounting (which may either be given as market-implied or be derived from a model of utility, consumption and production). In that sense, it is rather a generalisation than an alternative. The modelling approach has specific relevance for climate models, where discounting is an important aspect in assessing the severity of future events. Our model may result in non-decaying discount factors (negative discount rates) for certain scenarios.
