Pricing Under Estimation Risk

Financial product prices often depend on unknown parameters. Their estimation introduces the risk that a better informed counterparty may strategically pick mispriced products. Understanding estimation risk, and how to properly price it, is essential. We discuss how total estimation risk can be minimized by selecting a probability model of appropriate complexity. We show that conditional estimation risk can be measured only if the probability model predictions have little bias. We illustrate how a premium for conditional estimation risk may be determined when one counterparty is better informed than the other, but a market collapse is to be avoided. We use a simple example from pricing regime credit scoring, where a loan applicant and a single bank engage in a zero-sum game. We find that in large samples kernelized logistic regression is at least as accurate as commonly used default probability estimators such as logistic regression, and that it has little bias. This allows estimating conditional estimation risk. Computations are fast using a model-based approach. These methods are empirically examined on a panel data set from a German credit bureau, where we also study dynamic dependencies such as prior rating migrations and defaults.