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

Journal of Real Estate Finance and Economics, Forthcoming

Posted: 8 Mar 2020

See all articles by Bilgi Yilmaz

Bilgi Yilmaz

Middle Eastern Technical University Ankara

Sevtap Kestel

Independent

Date Written: February 11, 2020

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 options 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.

Keywords: Mortgage default risk; Mortgage prepayment risk; Malliavin calculus; hedging coefficients; Monte Carlo simulation

Suggested Citation

Yilmaz, Bilgi and Kestel, Sevtap, Computation of Hedging Coefficients for Mortgage Default and Prepayment Options: Malliavin Calculus Approach (February 11, 2020). Journal of Real Estate Finance and Economics, Forthcoming , Available at SSRN: https://ssrn.com/abstract=3536561

Bilgi Yilmaz (Contact Author)

Middle Eastern Technical University Ankara ( email )

Ankara
Turkey

Sevtap Kestel

Independent ( email )

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