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

Author

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  • Bilgi Yilmaz

    (Middle East Technical University)

  • A. Sevtap Selcuk-Kestel

    (Middle East Technical University)

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.

Suggested Citation

  • Bilgi Yilmaz & A. Sevtap Selcuk-Kestel, 2019. "Computation of Hedging Coefficients for Mortgage Default and Prepayment Options: Malliavin Calculus Approach," The Journal of Real Estate Finance and Economics, Springer, vol. 59(4), pages 673-697, November.
    • Handle: RePEc:kap:jrefec:v:59:y:2019:i:4:d:10.1007_s11146-018-9688-6
    DOI: 10.1007/s11146-018-9688-6
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    Cited by:

    1. Bilgi Yilmaz & Ralf Korn & A. Sevtap Selcuk-Kestel, 2023. "The Impact of Large Investors on the Portfolio Optimization of Single-Family Houses in Housing Markets," Computational Economics, Springer;Society for Computational Economics, vol. 61(2), pages 855-873, February.
    2. Ralf Korn & Bilgi Yilmaz, 2022. "House Prices as a Result of Trading Activities: A Patient Trader Model," Computational Economics, Springer;Society for Computational Economics, vol. 60(1), pages 281-303, June.

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