The Pricing of Mortgage Insurance Premiums Under Systematic and Idiosyncratic Shocks

• Author: Ming Pu,Gang‐Zhi Fan,Chunsheng Ban
• Published date: 01 June 2016
• DOI: http://doi.org/10.1111/jori.12052
• Date: 01 June 2016

THE PRICING OF MORTGAGE INSURANCE PREMIUMS UNDER

SYSTEMATIC AND IDIOSYNCRATIC SHOCKS

Ming Pu

Gang-Zhi Fan

Chunsheng Ban

ABSTRACT

The recent financial crisis has posed new challenges to the pricing issue of

mortgage insurance premiums. By extending an option-based approach to

this pricing issue, we attempt to tackle several key challenges including the

clustering of mortgage defaults, the diversification effect of underlying

property pools, and mortgage insurers’ information advantages. Our model

partitions the volatility of collateralized property prices into idiosyncratic

volatility and systematic volatility. Our results demonstrate that although

the rising number of pooled mortgage loans can reduce the volatility of

average default losses, the increasing correlation between the collateralized

properties can lead to the volatility clustering of these losses.

INTRODUCTION

The 2008 U.S. government bailout of the insurance giant American International

Group has aggravated our concern regarding the impact of the recent financial crisis

upon the insurance sector. Even though this crisis originated from the residential

mortgage market, it quickly spread its adverse impact to many other sectors and led

to a global economic slowdown. Among the various causes associated with the crisis,

Ming Pu is at the School of Insurance and Collaborative Innovation Center of Financial Security,

Southwestern University of Finance and Economics, 55 Guanghuacun Street, Chengdu, China.

Gang-Zhi Fan is at the Department of Real Estate Studies, Konkuk University, 120 Neungdong-

ro, Gwangjin-gu, Seoul 143-701, Korea. Gang-Zhi Fan can be contacted via e-mail:

fan10@konkuk.ac.kr. Chunsheng Ban is at the Department of Mathematics, Ohio State

University, 100 Math Tower, 231 West 18th Avenue, Columbus, OH 43210-1174. USA. We

would like to thank Gene C. Lai, Sheng Xiao, two anonymous referees, and seminar participants

at the 16th International Congress on Insurance: Mathematics and Economics and the 2012

Asian Real Estate Society-American Real Estate and Urban Economics Society Joint

International Conference for helpful comments. This work was supported by the National

Research Foundation of Korea (NRF) grant funded by the Korean government (NRF-

2014S1A5A8012340).

© 2014 The Journal of Risk and Insurance. Vol. 83, No. 2, 447–474 (2016).

DOI: 10.1111/jori.12052

447

the clustering outbreak of mortgage defaults has been widely identified as one of the

main causes leading to the crisis (e.g., Harrington, 2009). This has posed new and

considerable challenges to the policy design and pricing issue of mortgage insurance

businesses. In addition to the clustering of mortgage defaults, several other key

challenges can be identified, from the relevant literature, to include systemic risk

impact (e.g., Harrington, 2009; Baluch, Mutenga, and Parsons, 2011), mortgage

lenders’ or insurers’ information advantages (Pu, Fan, and Deng, 2014), and the

diversification effect of mortgage pools (e.g., Calem and LaCour-Little, 2004; Buckley

et al., 2006). Due to the considerable importance of mortgage insurance policies in

addressing the problems of mortgage defaults, this article attempts to investigate the

pricing issue of mortgage insurance premiums by allowing for the important

implications of these challenges.

Mortgage insurance can typ ically be defined as a category of insurance agreements

or policies whereby the char tered mortgage insurers provide cove rage for the default

losses of mortgage loans. Fo r the purpose of this study, we focus our attentio n on the

typical category of insuran ce contracts rather than th e later-developed credit

derivatives, while mortg age default risk can also be hedged using the credit

derivatives such as credit defau lt swaps.

1

Under the insurance policies, policy-

holders are required to pay mo rtgage insurance premiums in exchange for cover age

of the default loss of mortgage loan s. The past four decades have seen a sustai nable

development in the U.S. mortgage insurance market. In the United States, several

major government agencie s such as Federal Housing Adm inistration and the

Department of Veteran Aff airs provide public insur ance services for home

mortgage loans, whose premiu ms are usually paid by the mortgage lenders. The

private insurance companie s can also offer private insur ance policies that

compensate the lenders for th e possible default losses of mortgage loans, while

these private mortgage in surance policies can be clas sified as either lender-pa id or

borrower-paid. In addition to the mortgage insurers, wh en mortgage borrowers or

lenders are required to enter in to an insurance contract, they are naturally conce rned

with how much premiums need t o be paid for the mortgage insurance policies. Suc h

concerns motivate insurance an d real estate scholars to examine the pricing issue of

mortgage insurance. Bruec kner (1985) provides an earl ier investigation on the

valuation of the costs of mort gage insurance. Brueckner’ s model emphasizes the

importance of taking the uncer tainty of future property price s into consideration

when pricing the insurance premiums of mortgage loans . Other studies have

developed option-based pr icing models for pricing th e insurance premiums of

mortgage loans. These mod els, such as Kau, Keenan, and Mu ller (1993), Kau and

Keenan (1995, 1996), Bardhan, K arapandz

ˇa, and Uros

ˇevic

´(2006), and Chen et al.

(2010), typically assume that the underlying house pric es evolve following a

geometric Brownian motion p rocess such that the option- pricing approach can be

applied to the valuation of the ex pected default loss and default probability of

1

Although a credit default swap, essentially, is also like an insurance contract, it is different

from the traditional category of insurance contracts in numerous important aspects such as the

number of covered objects, insurable interest, and regulatory jurisdiction (Schmaltz and

Thivaios, 2012).

448 THE JOURNAL OF RISK AND INSURANCE