Default and prepayment risk management using option based mortgage contract pricing method

Yılmaz, Bilgi
Kestel, Sevtap Ayşe
Mortgage is an important factor in real estate business. The deals done based on the long-term investments, consider real estates as an option to secure the future investments, such as in life insurance, pension savings and reverse mortgage agreements. This study aims pricing a mortgage contract based on the modeling on a financial instrument. It consists of two main parts: (i) The option based mortgage contract pricing is introduced using a two-state bivariate diffusion stochastic model which has two important advantages. First, within this framework, PDEs and finite difference methods are available for the computation of the mortgage contract prices. Second, it allows a simple description of the correlation between volatility movements and returns, which is parameterized by the correlation coefficient of the two Wiener processes. (ii) Exploring the hedging coefficients of the mortgage default and prepayment options, which are embedded into mortgage contracts based on the change in spot rate and underlying house price to manage the default and prepayment risk. Having these two aims, we use the finite-dimensional Malliavin calculus, since the distribution of both options are unknown, their payoffs are non-differentiable and more importantly, numerical solution of mortgage PDEs may not be required. Naturally, we obtain the hedging coefficients as a product of option’s payoff and an independent weight, which permit us to derive estimates by running a Monte Carlo (MC) algorithm. The simulations reveal that the default and prepayment options are both more sensitive to changes in spot rate than changes in the underlying house prices
Citation Formats
B. Yılmaz and S. A. Kestel, “Default and prepayment risk management using option based mortgage contract pricing method,” presented at the 4 th European Actuarial Journal Conference (2018), Leuven, Belgium, 2018, Accessed: 00, 2021. [Online]. Available: