Computation of Hedging Coefficients for Mortgage Default and Prepayment Options: Malliavin Calculus Approach

Abstract

This study explores the hedging coefficients of the financial options to default and to prepay embedded into mortgage contracts based on the change in spot rate, underlying house price and its volatility. In the computations, the finite-dimensional Malliavin calculus is applied since the distribution of both options is unknown and their payoffs are non-differentiable. Naturally, the hedging coefficients are obtained as a product of option's payoff and an independent weight, which permits the user to derive estimations for the hedging coefficients by running a crude Monte Carlo (MC) algorithm. The simulations reveal that the financial options to default and to prepay are both more sensitive to a change in spot rate than a change in underlying house price and its volatility. There are two potential usages of the hedging coefficients: first, they allow the user to determine the effects of spot rate and underlying house price change and its volatility on the default and prepayment options, and second, borrowers and lenders can replicate and hedge their main portfolio by using the balance between these coefficients and the default and prepayment options.

Forecasting house prices in Turkey: GLM, VAR and time series approaches

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“…As commodity gold prices is one of the most influential investment tools in Turkey. In many studies, it is proven that inflation and real estate markets are highly dependent on each other and investing in the real estate market may protect the capital against inflation (Yilmaz, 2019;Yilmaz and Selcuk-Kestel, 2019). Therefore, we take into account inflation and fixed-rate mortgage (FRM) since house prices require most buyers to finance through loan.…”

The Effect of Selected Macroeconomic Variables on the Housing Price Index in Turkey

“…On the one hand, In Turkish market, gold, foreign exchange and inflation are effective factors compared with the others. On the other hand, in developed countries such as USA, mortgage rate is dominant factor (Yilmaz & Selçuk-Kestel, 2019). The study related to the relationship between inflation and house prices in 26 regions in Turkey, regional differences are important and the policies must be adapted accordingly.…”

The Impact of Large Investors on the Portfolio Optimization of Single-Family Houses in Housing Markets

“…By relying on the efficient market hypothesis in the modern portfolio theory, we may claim the price of a house mirrors all available information in the housing market, which leads us to use the diffusion process as in the studies (Kau et al 1995(Kau et al , 1990Miranda-Mendoza 2010), and (Yilmaz and Selcuk-Kestel 2019). Therefore, it is likely the price of the house is indifferent to the type of purchaser whether the buyer is a large or an individual investor (Allen Marcus et al 2018).…”