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주택가격이 모기지 대출 조기상환율에 미치는 영향에 관한 연구 : 2-요인 구조모형 접근법

  • 엄영호 연세대학교 경영대학 교수
  • 한영하 NICE P&I 평가사업본부 본부장
  • 한재훈 연세대학교 경영대학 교수
본 연구는 한국주택금융공사 보금자리론 풀을 대상으로 합리적 조기상환을 가정하는 이론모형을 통해 조기상환율을 추정하고 분석하는 것을 목적으로 한다. 연구대상 풀은 2010년 12월 기준 최소 관측치가 30개가 넘는 34개 풀이며 조기상환 관측치는 1,877개 관측치를 활용하였다. 이론모형은 금리요인 외에 주택가격을 상태변수로 도입하며, 모기지 차입자의 이질성을 명시적으로 고려하는 Downing, Stanton, and Wallace(2005) 모형을 적용하되 주택가격이 하락하는 경우 뿐 아니라 상승하는 경우에도 조기상환율에 영향을 미칠 수 있도록 조기상환 위태율 구조를 변형하여 조기상환율을 추정하였다. 조기상환율 추정 시 금리요인 외에 주택가격을 상태변수로 포함하는 경우와 포함하지 않는 경우를 구분하여 분석하였다. 실증분석결과 모기지론의 조기상환율을 설명하는 요인으로서 금리변수와 함께 주택가격변수 역시 통계적으로 유의하게 추정되었다. 위태율 모수구조에 있어 Downing et al.(2005)과 같이 주택가격을 가격하락에 따른 부도요인에만 영향을 미치는 방식으로 설정하는 경우에는 조기상환율을 설명하기 어려웠으며 주택가격 상승도 조기상환율에 영향을 미칠 수 있도록 설정된 변형된 위태율 모수구조에서는 추정 결과가 우수하였다. 국내의 경우 부도요인 효과가 유의하지 않은 이유는 연구 대상기간(2004년~2010년)동안 주택가격이 큰 폭으로 하락한 경험이 없고 모기지론 대출시장에서 보수적인 LTV(Loan-To-Value)가 적용되어 온 것에 기인하는 것으로 판단된다.
조기상환율; 모기지론 가치; 금리; 주택가격; 내재옵션가치; Mortgage Prepayment; Default Option; Interest Rate; House Price; Structural Models

The Effect of House Prices on Mortgage Prepayment in Korea : A Two-Factor Structural Approach

  • Young Ho Eom
  • Youngha Han
  • Jaehoon Hahn
We estimate a two-factor structural mortgage valuation model using data on pool-level termination rates for fixed-rate mortgage loans issued by the Korea Housing Finance Corporation (KHFC) between 2004 and 2008. Our model is a modified version of that proposed by Downing, Stanton, and Wallace (DSW, 2005), in which borrowers rationally decide when to prepay and default in response to changes in house prices as well as interest rates. DSW (2005) find that incorporating house price movements into the model significantly improves its ability to match historical prepayment data over Stanton’s (1995) one-factor (interest rate only) model. In DSW (2005), house price changes are modeled to affect borrowers’ termination behavior only when prices decline by increasing the value of default option, but this particular specification does not bode well for our Korean sample period, during which house prices did not experience substantial or sharp declines. Consequently, we modify DSW’s (2005) two-factor model so that house price movements influence termination behavior when prices increase as well as when prices decline. In contrast to the structural model used in this paper, previous empirical research on mortgage prepayment in Korea has mostly used statistical models, in which termination behavior is modeled as a function of a set of exogenous variables such as interest rates and house prices that represent the factors affecting prepayment and default. While such statistical approach may produce estimated prepayment rates that are closer to the historical data, its out-of-sample forecasting power is likely to be low, and the model is not suitable for pricing mortgage-backed securities. The structural approach taken in this study, on the other hand, models prepayment and default as a rational borrower’s optimal responses to the changes in interest rates and house prices that represent the model’s state variables. Such structural models should perform better out of sample than statistical models, and they can be used in the valuation of mortgage-backed securities. The mortgage prepayment data used in this study are from 34 pools of fixed-rate mortgage loans (called Bogeumjari loans) issued by the KHFC. The sample period is from June 2004 to December 2010, and the prepayment rates at the pool-level, as published monthly by the KHFC, are used. The empirical results show that both interest rates and house price changes significantly affect prepayment rates. In particular, house prices and prepayment rates have a positive association, consistent with Park and Bang (2011) and Choi and Kim (2011), who use statistical models. In addition, incorporating house price movements into the model improves its performance in matching historical prepayment rates, compared to the model in which only interest rate movements are considered. The results of Davidson and MacKinnon’s (1981) J-test selecting between non-nested models show that the two-factor specification that includes house prices and interest rates is better for estimating prepayment rates than the one-factor (interest rate) specification. Moreover, we find that the two-factor model produces prepayment forecasts that are closer to the historical data than the one-factor model in an out-of-sample test. In a structural model, mortgage terminations (prepayment or default) are the result of borrowers’ optimizing behavior, and house price movements can affect the borrowers’ termination behavior as follows. When house prices fall, the value of the default option implicitly held by the borrower increases. And the movements in the value of the default option significantly affect the value of the borrower’s prepayment option and therefore, the likelihood of prepayment. However, we find that prepayment rates decrease with declining house prices. The house prices in Korea experienced some declines during our sample period, but not by any substantial degree. Our finding of lower prepayment rates in times of declining house prices is similar to Mattey and Wallace (2001), who find that weak house prices tend to depress refinancing and prepayments. When house prices increase, so does the collateral value of the houses and the value of the borrower’s equity, which influences the likelihood of prepayment if, for example, the borrower wants to cash out some of the increase in equity. This argument is consistent with the higher prepayment rates during times of increasing house prices found in this paper. More specifically, the period of increasing house prices in our sample is from late 2006 to early 2007, which coincides with rising interest rates. Despite the rising interest rates and penalties for prepayment, prepayment rates during that period increased in close association with rising house prices, suggesting that both interest rates and changes in house prices significantly affect mortgage prepayment rates in Korea.