Funded by Scientific and Technical Research Council of Turkey (TÜBİTAK), 2007-2009

Coordinator: Işıl Erol (Department of Economics and Institute of Applied Mathematics, Middle East Technical University, Ankara)

Researchers:

  1. Ömür Uğur (Institute of Applied Mathematics, Middle East Technical University, Ankara)
  2. Kasırga Yıldırak (Institute of Applied Mathematics, Middle East Technical University, Ankara)

Assistant: Özgenay Çetinkaya (Institute of Applied Mathematics, Middle East Technical University, Ankara)

Abstract

Attempts to value options and other derivatives have a long history. The great breakthrough was registered only in the beginning of the 1970s with the publication of papers by Black and Scholes and by Merton. Under some strong assumptions about interest rate and volatility behaviour, both articles provide closed-form solutions to the valuation of simple options on stocks. Following these seminal works, a new approach to finance has been under development. Option pricing models extended and applied the conceptual setting of these authors to the valuation of all types of explicit and embedded options. Over the last two decades, option pricing models have been extensively used both by the practitioners and academicians for pricing the mortgages and mortgage-related products in most developed countries, especially in the US. This is because the mortgage market became the largest component of the fixed income securities market in the US capital markets. Extant literature shows that option-pricing models are only applied to mortgage contracts originated in developed markets under stable economic environments

This project will be the first attempt to price the standard fixed-rate mortgage (FRM) contracts in a developing economy like Turkey. In fact, mortgage financing is a fundamental part of financial sector development in developing economies. However, there is not an extensive academic research focused on examining the performance of mortgage contracts in developing countries, especially in high inflation economies. The main objective of this project is to price both the default risk and the prepayment risk of the FRMs that are currently originated by the Turkish banks using the well-known option pricing models.

Turkey has a rapidly growing sector for housing loans since the late 1990s. Especially during the last few years, the banking sector has expanded the mortgage loan products significantly. However, there is not any academic research, to the best of our knowledge, to analyse these financial instruments with their embedded options to default and prepay the loan. In developed economies, the insurance companies provide default risk management in mortgage markets. Currently, there are not any mortgage insurance contracts traded in the Turkish financial markets. This project also aims to price mortgage insurance product as a potential financial derivative in the Turkish capital markets.

We believe that our project will have important implications both for the academic literature and the Turkish banking sector. The main contributions can be summarized as follows. In the extant literature, this project will be the first attempt to use the classical option pricing model to price mortgage contracts in a developing country with high inflation risk. Second, due to the high inflation risk, interest rates will be modeled by jump diffusion models instead of the classical diffusion models used widely in the literature. A numerical analysis of the Partial Integro Differential Equation (PIDE) for jump processes will be used for the first time to price FRMs in inflationary economies. Third, this project will be one of the initial applications of financial mathematics to the financial sector of the Turkish economy. In particular, numerical analysis of applied partial differential equations will be used to price mortgage contracts with their embedded options. Lastly, in the Turkish financial markets, there are not any mortgage insurance products. This project will answer the question of “What will be the bank’s (lender’s) position if they have mortgage insurance products?”.

The project is for twenty four months and will be conducted by three researchers. The project will be carried out on the basis of developing an algorithm for pricing the FRMs with their embedded options under both relatively stable economic conditions of the recent years and the potential inflationary environment in the near future. As a numerical solution technique, we will use a backward pricing methodology that includes dynamic programming. Numerical results obtained will be evaluated under different economic scenarios.

The subject of the project is a very new topic in mortgage pricing literature. The characteristic value of this project is its contribution of new ideas and methods to price a classical mortgage contract in high inflation economies. There is no doubt that the results of the project will be valuable enough to be published in respected journals, books and conferences covered in scientific indexes.

Keywords: option pricing models, fixed-rate mortgage contract, default option, prepayment option, mortgage insurance, numerical solutions to partial differential equations