Pricing Mortgage Insurance with Asymmetric Jump
Risk and Default Risk: Evidence in the U.S.
Published online: 8 March 2011
Springer Science+Business Media, LLC 2011
Abstract This study provides the valuation of mortgage insurance (MI) considering
upward and downward jumps in housing prices, which display separate distributions
and probabilities of occurrence, and the mortgage insurer’s default risk. The
empirical results indicate that the asymmetric double exponential jump diffusion
performs better than the log-normally distributed jump diffusion and the Black-
Scholes model, generally used in previous literature, to fit the single-family
mortgage national average of all home prices in the US. Finally, the sensitivity
analysis shows that the MI premium is an increasing function of the normal
volatility, the mean down-jump magnitudes, the shock frequency of the abnormal
bad events, and the asset-liability structure of the mortgage insurer. In particular, the
shock frequency of the abnormal bad events has the largest effect of all parameters
on the MI premium. The asset-liability structure of the mortgage insurer and shock
frequency of the abnormal bad events have a larger effect of all parameters on the
default risk premium.
Keywords Mortgage insurance contract
Asymmetric double exponential jump
JEL Classification G1
J Real Estate Finan Econ (2012) 45:846–868
Department of Finance, National Kaohsiung University of Applied Science, 415 Chien Kung Road,
Sanmin District, Kaohsiung 80778, Taiwan, R.O.C.
Fubon Financial, 3F., No.9, Xiangyang Rd., Zhongzheng Dist., Taipei 100, Taiwan, R.O.C.
S.-D. Shyu (*)
Department of Finance, National Sun Yat-sen University, No. 70, Lienhai Rd., Kaohsiung 80424,