Bezpieczny Bank

Juliusz Jabłecki
University of Warsaw and National Bank of Poland

The value of a prepayment option in a fixed rate mortgage: Insights from breakeven volatility

Abstract

This paper presents a novel approach of estimating the value of a prepayment option in a fixed rate loan based on the concept of breakeven volatility. Since the prepayment option can be exercised essentially at any time prior to maturity, its valuing requires: (i) a pricing model sophisticated enough to handle its early exercise feature; and (ii) a broad set of interest rate derivatives prices to which the model can be calibrated to preclude arbitrage. This paper shows that when the derivatives market is not developed enough to ensure calibration, a good approximation of the fair value of a prepayment option can be derived by constructing the “missing” derivatives prices by back-testing delta hedged swaptions. This produces a “fair” volatility surface conditioned on the realized historical zero coupon bond prices and swap rates, which can be used to calibrate the prepayment option pricing model. The paper presents numerical examples for the Polish market as of January 2017. The mortgage spread component related to the prepayment option price proves to be quite significant, stressing the importance of an adequate risk management of the inherent callability feature and possibly explains why fixed rate mortgage products have struggled to develop in Poland so far.

Key words: prepayment, fixed rate loan, Bermudan swaption, breakeven volatility, Cheyette model

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