Certain bank loans pay a spread above a floating-rate interest rate (typically LIBOR) subject to a floor. I would like to find the value of this floor to the investor. Assume for this example that the loan does not have any default (credit) risk.
As a first pass, the value of the floor could be approximated using the Black model to price a series of floorlets maturing on the loan's payment dates. However, the borrower has a right to refinance (call) the loan (suppose it is callable at par), subject to a refinancing cost. If interest rates decline and the floor is in the money, the borrower is more likely to call the loan. Thus the floor (along with the rest of the loan) is more likely to go away precisely when the investor values it more.
How can this floor be valued?
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