How the Pricing Kernel Transforms Real Probabilities into Risk-Neutral Probabilities

Summary

The answer explains the link between real-world probabilities and risk-neutral probabilities through the marginal rate of substitution. A future payoff is valued by weighting it with a pricing kernel, expressed in the example as discounted marginal utility relative to current marginal utility. This connects asset prices to investors’ preferences and to how payoffs covary with future wealth.

Normalizing the pricing kernel produces a probability density that adjusts the real-world density; under that adjusted distribution, the price can be written as a discounted expected payoff. The explanation notes that linear utility makes marginal utility constant, while payoffs independent of future wealth can also have the ordinary discounted expectation form. These are conceptual illustrations, not an empirical method for estimating the kernel. The result depends on the assumed utility and wealth relationship, and the response does not compare alternative models or provide references beyond the question’s framing.

Key ideas

• The pricing kernel weights future cash flows by discounted marginal utility.
• Normalizing the pricing kernel converts the real probability density into a risk-adjusted density.
• Risk-neutral pricing expresses value as a discounted expectation under that adjusted distribution.
• Linear utility makes marginal utility constant, while wealth-independent payoffs can also have ordinary discounted expected values.
• The adjustment depends on how payoffs relate to future wealth and on the assumed utility function.

Tags

# Credit scoring: combining application and behavior scoring


# Credit scoring: combining application and behavior scoring












The aim in credit scoring is to distinguish good clients from bad clients. This is done at the stage of the application (application scoring - AS) based on demographic and similar data. AS is used to decide whether the application is accepted or rejected.

When the credit is being repayed the bahavior of the obligor (did s/he need any reminders, ...) is used to calculate a behavior scoring (BS). The BS can be used to estimate needed reserves for the credit given and for further credit descisions

It is known (and clear) that the discriminatory power of AS deteriorates in the months after the application. Thus it is good practice to combine AS and BS.

What are best practices about when to combine AS and BS and how to do this? I am looking for references and opinions in the context of banking credit risk.

Machine learning like aspects are very important and interesting but I would be happy to have the banking context too. Thanks a lot !

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.