Pricing the Default Option of Inflation-Indexed Mortgages Using Explicit Finite Difference Method

This paper evaluates the default risk of civil servants' wage-indexed payment mortgage (WIPM) contract in Turkey, which is linked to the expected inflation. The aim of the study has two sides: one is to apply the contingent claims approach, which has been widely used to price standard fixed-and adjustable-rate contracts, to price an inflation-indexed mortgage. The second is to understand if WIPM contract is a suitable mortgage design for lenders under an inflationary economy. We extend the traditional risk-neutral valuation for pricing the WIPM contract with its embedded default option. Using backward pricing method, namely the explicit finite difference method, we evaluate this unique inflation-indexed mortgage contract from the lender's point of view. The expected inflation and house price are the two stochastic variables underlying the WIPM contract. Our numerical results show that the lender benefits from originating WIPM only during the periods when the real interest rate is very low. Expected inflation risk premium notably increases the value of future payments on WIPM contract, resulting in high values of lender's position in the mortgage agreement. The results also show that house price volatility has a greater effect on the borrower's default option value compared to the expected inflation volatility