What can we recover from the data?

At the UnRisk Academy events, there is typaically at least one session on parameter identification, just as it has been at the Frankfurt and Zurich events.

From my understanding, the typical workflow in quant work is

1. Choose a model for the underlying
2. Given prices of liquid instruments, calibrate the parameters of this model
3. Use the parameters to valuate something more complex than the vanilla things.

The second step is a classical inverse problem, and we should ask ourselves questions about existence, uniqueness and stability.

In a sequence of forthcoming posts, I will cover some examples from finance.

We, at MathConsult and UnRisk, have been working on a wide range of inverse problems in the past. Some examples are:

• Identification of cooling strategies in continuous casting of steel
• Tomography of the atmosphere for astronomical applications
• How thick is the wall of a blast furnace?