2017 | 4 (69) | 65-87
Article title

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

Title variants
Languages of publication
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.
Physical description
  • Uniwersytet Warszawski
  • Agarwal S., Driscoll J.C., Laibson D.I., Optimal Mortgage Refinancing: A Closed-Form Solution, Journal of Money, Credit and Banking 2013, 45(4), pp. 591–622. Atiya A.F., Wall S., An analytic approximation of the likelihood function for the Heston model volatility estimation problem, Quantitative Finance 2009, 9(3), pp. 289–296.Black F., Scholes M., The pricing of options and corporate liabilities, Journal of Political Economy 1973, 81(3), pp. 637–654. Brigo D., Mercurio F., Interest rate models-theory and practice: with smile, inflation and credit, Springer Science & Business Media 2007. Cheyette O., Term structure dynamics and mortgage valuation, The Journal of Fixed Income 1992, 1(4), pp. 28–41.Collin-Dufresne P., Harding J.P., A closed form formula for valuing mortgages, The Journal of Real Estate Finance and Economics 1999, 19(2), pp. 133–146. Cox J.C., Ingersoll Jr J.E., Ross S.A., A theory of the term structure of interest rates, Econometrica: Journal of the Econometric Society 1985, pp. 385–407. Davidson A., Levin A., Mortgage Valuation Models: Embedded Options, Risk, and Uncertainty, Oxford University Press 2014. Dupire B., Pricing with a smile, Risk 1994, 7(1), pp. 18–20. Dupire B., Fair Skew: Break-Even Volatility Surface, Discussion paper, Bloomberg 2006. Gatarek D., Jabłecki J., A local volatility model for swaptions smile, Journal of Computational Finance 2016, Forthcoming. Gatarek D., Jabłecki J., Qu D., Non-parametric local volatility formula for interest rate swaptions, Risk 2016, pp. 120–124. Heston S.L., A closed-form solution for options with stochastic volatility with applications to bond and currency options, Review of Financial Studies 1993, 6(2), pp. 327–343. Kau J.B., Keenan D.C., An overview of the option-theoretic pricing of mortgages, Journal of Housing Research 1995, 6(2), p. 217. Longstaff F.A., Schwartz E.S., Valuing American options by simulation: a simple leastsquares approach, Review of Financial studies 2001, 14(1), pp. 113–147. Qu D., Manufacturing and managing customer-driven derivatives, John Wiley & Sons, Chichester 2016, West Sussex, United Kingdom.
Document Type
Publication order reference
YADDA identifier
JavaScript is turned off in your web browser. Turn it on to take full advantage of this site, then refresh the page.