# Optimal Stopping Pricing Problem

#### bananaman

Hi,

I am working on a mark to market valuation model of an illiquid fixed income instrument. I am omitting lots of assumptions coming from the business side, and over-simplifying, but it boils down to an optimal stopping problem.

My instrument has a set series of quarterly cash flows, calculated outside of the model. From certain date onwards (in several years), I can exit that stream of cash flows at any quarter for a lump sum payment, which is a function of discount margins (of few other illiquid instruments) at that moment and the other variable being that date. Obviously, the exit would be executed once it is optimal which is decided each quarter. I am only looking for the valuation of such instrument.

What I have:

discount rate (fixed) for valuation of my instrument,
function which translates few variables of discount margins at any given point in time into the exit cash flow,
for simplicity assuming all DMs are perfectly correlated,
long series of cash flows assuming no exit,
the earliest possible exit date,
trailing 12 months of historic data for these DMs (12 data points for each, this would be expanded over time)

My idea is to run the observed standard deviations on these DMs, and based on them and the current DM value to studentise all DMs as a function of one z-score variable.
Second step is to model this z-score variable with Cox Ingersoll Ross model. I am not sure though that this is appropriate as DMs are not exactly interest rates. (hints on how do to this are helpful)
I am not sure how to approach the next step to use the assumption about the variable being Cox Ingersoll Ross for pricing this option. It should be fairly simple though.

I am not a pro quant, but did some econometrics at school and can get my head around some of the more basic stuff.

Any hints or observations would be helpful.

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