Pricing default and prepayment risks of fixed-rate mortgages in turkey : an application of explicit finite difference method

Çetinkaya, Özgenay
The mortgage system has been used for many years in many countries of the world. Although the system has undergone many changes over the passing years, the basics remain the same. So, it can be thought that the earlier systems form the basis of today’s mortgage system even though it represents some differences in practice among the countries. However, this system is very new for Turkish financial market as compared with developed countries. The aim of this study is estimating the default and prepayment risk of mortgage contract and pricing the contract in emerging markets like Turkey. In this study, a classical option pricing technique based on Cox, Ingersoll and Ross [8] is used in order to evaluate Turkish fixed-rate mortgages. In this methodology, the spot interest rate and the house price are used as state variables and it is assumed that the termination decision of mortgage is driven by a economic rationale. Under this framework, the model evaluates the embedded options, namely prepayment and default options, and the future payments which corresponds to the mortgage monthly payments. Another aim of this study is the pricing of mortgage insurance policy which has not been used yet in Turkish mortgage market but thought as potential derivative in this market. Therefore, the model used in the study also provides values for mortgage insurance policy. The partial differential equation which is derived for the mortgage, its components and mortgage insurance policy does not have closed form solutions. To cope with this problem, an explicit finite difference method is used to solve the partial differential equation. Numerical results for the value of mortgage-related assets are determined under different economic scenarios. Results obtained in the basic economic scenario show that Turkish banks apply lower contract rates as compared with the optimal ones. This observation indicates that the primary mortgage market in Turkey is still in its infancy stage. Numerical results also suggest that it is beneficial for the lenders to have mortgage default insurance, especially for the high LTV ratio mortgages.
Citation Formats
Ö. Çetinkaya, “ Pricing default and prepayment risks of fixed-rate mortgages in turkey : an application of explicit finite difference method,” M.S. - Master of Science, Middle East Technical University, 2009.