Fixed-Rate Endowment Mortgage and Mortgage Indemnity Valuation
36 Pages Posted: 20 Mar 2002
Date Written: January 2002
Fixed rate endowment mortgages differ from fixed rate repayment mortgages primarily because, in the event of early termination, the amount owed by the borrower is a function of the evolution of the term structure of interest rates, whereas for a repayment mortgage it is pre-determined.
We use a contingent claims framework for valuing the embedded options in certain British fixed-rate endowment mortgages, with a (capped) mortgage indemnity guarantee (MIG). We assume a mean-reverting interest rate and a lognormal house price diffusion process to arrive at a partial differential equation as the basis of the contingent claims and include conventional mortgage terms such as arrangement fees and prepayment penalties.
This methodology provides a template for the borrower, lender and insurer to compare mortgage terms, including the fairness of contract rates, fees and any MIG premiums required, when borrowing more than 75% of the house value at origination. Given the conventional terms and the diffusion processes, we assume the parties have common expectations for some diffusion parameters, including expected future rate and price volatilities. Also we assume that borrowers are 'economic actors' regarding default and prepayment options, and that factors such as mobility, divorce, unemployment, and transaction costs are deterministic and can be ignored in this model, along with moral hazard problems between the insurer and the lender.
Since the partial differential equation incorporating the general features of these mortgage contracts does not have a closed-form solution, an explicit finite difference method is used for the valuation (and sensitivity) results. We provide graphical representations (and interpretations) of each mortgage component as a function of house prices and interest rate levels.
After empirical studies on the input parameters, each mortgage component may be compared with 'market values'. This model may also be useful as a 'mark-to-value' proxy for all parties, as expected parameters change (especially interest rate and house price levels, and expected future volatilities), for purposes of determining 'value added accounting', appropriate reserves, and indeed for setting premiums and business decisions. Finally, we compare endowment and repayment mortgages for different levels of loan-to-value ratios, interest rate and house price volatility.
Keywords: Endowment Mortgage, Mortgage Indemnity, Coinsurance
JEL Classification: G21
Suggested Citation: Suggested Citation