Differential default risk among traditional and non-traditional mortgage products and capital adequacy standards

We develop a framework to quantify credit risks of non-traditional mortgage products (NMPs). Ex ante probabilities of default are caused by willingness-to-pay and ability-to-pay problems and the high default rates for NMPs confirm that payment shock is a critical default risk indicator. Monte Carlo simulations are conducted using three correlated stochastic variables (mortgage interest rate, home price, and household income) under normal and stressed economies. Results confirm that the default risk of 2/28 and option ARM contracts requiring a minimum monthly interest payment have a greater probability of default than other mortgage products in all economic scenarios. Additionally, the credit risk of NMPs is primarily systematic risk, suggesting that these products should require higher risk-based capital. Due to the non-linear distribution of credit risk, even the advanced internal-based rating approach of the Basle II framework can understate the risk involved in these NMPs.     

Estimation of Housing Price Jump Risks and Their Impact on the Valuation of Mortgage Insurance Contracts

Housing price jump risk and the subprime crisis have drawn more attention to the precise estimation of mortgage insurance premiums. This study derives the pricing formula for mortgage insurance premiums by assuming that the housing price process follows the jump diffusion process, capturing important characteristics of abnormal shock events. This assumption is consistent with the empirical observation of the U.S. monthly national average new home returns from 1986 to 2008. Furthermore, we investigate the impact of price jump risk on mortgage insurance premiums from shock frequency of the abnormal events, abnormal mean and volatility of jump size, and normal volatility. Empirical results indicate that the abnormal volatility of jump size has the most significant impact on mortgage insurance premiums.     

Appraisal Quality and Residential Mortgage Default: Evidence from Alaska

We empirically examine the effect of appraisal quality on subsequent mortgage loan performance using data from the high volatility housing market of Alaska in the 1980s. We develop measures of appraisal quality by computing the residual between a hedonic estimate of house value using available information from other appraisals compared to actual ex ante appraised value. We then estimate proportional hazard models of mortgage default and find that several measures of appraisal quality, particularly appraised value in excess of hedonic estimates, are significantly related to default risk. Using valuations subsequent to loan default, we are also able to evaluate how well house price indices perform in terms of estimating current loan-to-value and offer some additional evidence on the controversy over the role of net equity versus trigger events as determinants of mortgage default. We also show that defaults are related to ex ante measures of housing market conditions, with additional implications for underwriting policies and the current industry trend away from traditional appraisal and toward automated valuation.     

Bias in an Empirical Approach to Determining Bond and Mortgage Risk Premiums

Empirical studies of bond and commercial mortgage performance often quantify a required risk premium by examining the difference between the promised yield and the realized yield as adjusted for default occurrence. These studies omit the effects of various other sources of risk, however, including collateral asset market risk, interest rate risk, and possibly call risk. These omissions downwardly bias the empirical risk premium estimate on the debt. In this paper, we disentangle and quantify the sources of this bias by modeling secured coupon debt (the commercial mortgage) as used in the calculation of a realized investment return. We consider deterministic and stochastic interest rate economies with mortgage contracts that are either noncallable or subject to a temporary prepayment lockout period. Given realistic parameter values associated with the term structure, underlying asset dynamics, and debt contracting, we show that the magnitude of the bias can be significant.     

Residential Mortgage Default: The Roles of House Price Volatility, Euphoria and the Borrower’s Put Option

House price volatility; lender and borrower perception of price trends, loan and property features; and the borrower’s put option are integrated in a model of residential mortgage default. These dimensions of the default problem have, to our knowledge, not previously been considered altogether within the same investigation framework. We rely on a sample of individual mortgage loans for 20 counties in Florida, over the period 2001 through 2008, third quarter, with housing price performance obtained from repeat sales analysis of individual transactions. The results from the analysis strongly confirm the significance of the borrower’s put as an operative factor in default. At the same time, the results provide convincing evidence that the experience in Florida is in part driven by lenders and purchasers exhibiting euphoric behavior such that in markets with higher price appreciation there is a willingness to accept recent prior performance as an indicator of future risk. This connection illustrates a familiar moral hazard in the housing market due to the limited information about future prices.     

Pricing Mortgage Insurance with Asymmetric Jump Risk and Default Risk: Evidence in the U.S. Housing Market

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.     

Identifying the determinants of mortgage default in Colombia between 1997 and 2004

This paper examines the relationship between mortgage default decisions and relevant observable variables in Colombia between 1997 and 2004. We estimate a discrete choice model of default using a panel of individual mortgage characteristics and payment information. We show that home prices and debt balances are the main determinants of mortgage default. We account for the presence of unobserved heterogeneity using Survey data and simulation techniques. Including controls for the distribution of income shows that income was not important but helps clarifying the relevance of mortgage leverage in the determination of the observed default rates.     

Correlated leverage and its ramifications

This paper develops a theory in which housing prices, the capital structures of banks (mortgage lenders) and the capital structures of mortgage borrowers are all endogenously determined in equilibrium. There are four main results. First, leverage is a “positively correlated” phenomenon in that high leverage among borrowers is positively correlated with high leverage among banks, and higher house prices lead to higher leverage for both. The intuition is that first-time homebuyers with fixed wealth endowments must borrow more to buy more expensive homes, whereas higher current house prices rationally imply higher expected future house prices and therefore higher collateral values on bank loans, inducing banks to be more highly levered. Second, higher bank leverage leads to greater house price volatility in response to shocks to fundamental house values. Third, a bank’s exposure to credit risk depends not only on its own leverage but also on the leverage decisions of other banks. Fourth, positive fundamental shocks to house prices dilute financial intermediation by reducing banks’ pre-lending screening, and this reduction in bank screening further increases house prices. Empirical and policy implications of the analysis are drawn out, and empirical evidence is provided for the first two main results. The key policy implications are that greater geographic diversification by banks, tying mortgage tax exemptions to the duration of home ownership, and increasing bank capital requirements when borrower leverage is high can help reduce house price volatility.     

House Price Markups and Mortgage Defaults

The transaction price of identical housing units can vary widely due to heterogeneity in buyer and seller preferences, matching, and search costs, generating what we term “markups” above or below the average market price. We measure markups for 3.4 million purchase-money mortgages and show that they can predict mortgage defaults and credit losses conditional on default even after accounting for collateral coverage (loan-to-value ratio) and a comprehensive set of other covariates. The findings suggest that standard collateral coverage estimation may be inaccurate, with implications for both individual and portfolio-level credit risk assessment.     

住房贷款违约风险定量分析初探

本首先剖析了影响住房贷款违约风险的主要因素，然后引入Merton的结构化模型来分析住房贷款在等额偿还方式下违约风险的度量问题，并从横向和纵向两个角度，通过模拟计算得出房价波动率和无风险利率对住房贷款的违约概率、预期损失和违约风险溢价的影响规律以及这三个指标在贷款期内的变化规律。     

The Effects of Purchases of Mortgages and Securitization by Government Sponsored Enterprises on Mortgage Yield Spreads and Volatility

In this paper, we investigate the effects of GSE (government sponsored enterprise) activities on mortgage yield spreads and volatility. Using various regression procedures (i.e., vector error correction (VEC) and GARCH models) and controlling for default and prepayment risk, we find that securitizations and purchases of mortgages by GSEs reduce mortgage yield spreads and volatility. In particular, we find that the yield spread between conforming and 10-year constant maturity treasury (CMT) rates decreases by 8.0 bp per $1billion increase in the level of GSE securitizations. Similarly, if GSEs increase mortgage purchases, the yield spread decreases 10.5 bp per $1billion increase of purchases. In addition, we hypothesize and find that GSE activities have a spillover effect to the non-conforming mortgage market; via investor substitutions, GSE purchases and securitizations of conforming loans reduce non-conforming loan rates. Thus, the measured influence of GSE activities is biased downward when measured using the spread of non-conforming loans over conforming loan rates. We also find that purchases of mortgages by GSEs significantly reduce mortgage yield volatility. In sum, our findings show that GSE activities reduce and stabilize mortgage market rates.     

A Model of Mortgage Default

In this paper, we solve a dynamic model of households' mortgage decisions incorporating labor income, house price, inflation, and interest rate risk. Using a zero‐profit condition for mortgage lenders, we solve for equilibrium mortgage rates given borrower characteristics and optimal decisions. The model quantifies the effects of adjustable versus fixed mortgage rates, loan‐to‐value ratios, and mortgage affordability measures on mortgage premia and default. Mortgage selection by heterogeneous borrowers helps explain the higher default rates on adjustable‐rate mortgages during the recent U.S. housing downturn, and the variation in mortgage premia with the level of interest rates.     

Mortgage Contracts,Strategic Options and Stochastic Collateral

This paper offers a game-theoretic model for both the analysis and valuation of mortgage contracts in the context of an economy with complete information and complete contingent claims markets. We analyze the equilibrium strategy of the lender, who holds an option over the magnitude of mortgage credit extended per dollar of collateral offered, and the mortgagor, who holds options to default or prepay, in a class of intertemporal mortgage contracts collateralized by property evolving according to a random process which is common knowledge to both parties to the mortgage contract. Using continuous–time arbitrage valuation principles, we derive the value of the mortgage contract to both parties and show, through both analytical solutions and numerical simulations, that Markov perfect equilibria exist in which, among other properties, a lower flow of housing services accruing to the borrower, per dollar of initial house value, and a correspondingly lower rate of effective depreciation, will elicit a larger volume of funds offered by a lender; the amount of credit offered, the values of the contract to both lender and mortgagor, and the expected losses to both parties from costly bankruptcy are highly sensitive to the perceived volatility of the value of the property collateralizing the mortgage, even in an economy with complete markets or risk neutrality on the parts of lender and borrower; the upper limit on mortgage credit offered by a rational lender may be a small fraction of the current fair market value of the property, regardless of the contractual yield offered by the borrower, and will decrease, at each such yield, as bankruptcy costs or housing service flows increase; and under significant but plausible values for bankruptcy and costs of liquidating property under foreclosure, the flow of mortgage credit can become negatively related to the spread of the mortgage yield over the riskless rate, with the lender preferring a lower contractual yield to a higher one.     

Local Traits and Securitized Commercial Mortgage Default

We expand on the standard commercial mortgage default model and create a new model by looking beyond the usual factors of option value, insolvency, property type, region, originator type, state foreclosure laws and macroeconomic measures. The new model incorporates measures of local economic conditions, specifically MSA-level commercial property market conditions, county level unemployment, and local home price appreciation. We estimate our new model using a dataset containing the performance histories of over 30,000 CMBS loans that were originated between 1998 and 2012. We find that those local trait variables affect the default rate of CMBS loans significantly and provide improved explanatory power over the standard model. We further explore the impact of local home price measures by comparing the explanatory power of lagged and contemporaneous home price indexes, comparing the power of home price indexes at the state, county, and zip-code level, examining the interaction of home price indexes with commercial property type, looking at the impact of home price indexes over time, and at the impact of introducing local commercial land price indexes. We find that local residential house price-related measures provide a high quality and high frequency signal of local market conditions.     

Extreme Events and the Copula Pricing of Commercial Mortgage-Backed Securities

Commercial mortgage-backed securities (CMBS), as a portfolio-based financial product, have gained great popularity in financial markets. This paper extends Childs, Ott and Riddiough’s (J Financ Quant Anal, 31(4), 581–603, 1996) model by proposing a copula-based methodology for pricing CMBS bonds. Default on underlying commercial mortgages within a pool is a crucial risk associated with CMBS transactions. Two important issues associated with such default—extreme events and default dependencies among the mortgages—have been identified to play crucial roles in determining credit risk in the pooled commercial mortgage portfolios. This article pays particular attention to these two issues in pricing CMBS bonds. Our results show the usefulness and potential of copula-based models in pricing CMBS bonds, and the ability of such models to correctly price CMBS tranches of different seniorities. It is also important to sufficiently consider complex default dependence structure and the likelihood of extreme events occurring in pricing various CMBS bonds.     

Theory and evidence on the dynamic interactions between sovereign credit default swaps and currency options

Using sovereign CDS spreads and currency option data for Mexico and Brazil, we document that CDS spreads covary with both the currency option implied volatility and the slope of the implied volatility curve in moneyness. We propose a joint valuation framework, in which currency return variance and sovereign default intensity follow a bivariate diffusion with contemporaneous correlation. Estimation shows that default intensity is much more persistent than currency return variance. The market price estimates on the two risk factors also explain the well-documented evidence that historical average default probabilities are lower than those implied from credit spreads.     

住房抵押贷款提前还贷风险管理研究

从现代金融和风险管理角度看,住房抵押贷款提前还贷对商业银行是一种期权性风险,对其收取违约金并非国际惯例,也并不是有效的风险补偿方式。商业银行应适应市场竞争需要,接受风险转嫁并提供风险管理服务,运用风险定价技术在按揭交易价格中对提前还贷风险进行补偿。对于已承担的风险,商业银行应构建抵押贷款提前还贷的数据库,通过表内对冲和市场对冲,推出多样化的住房抵押贷款方式,积极推进住房抵押贷款证券化,从而最终增强银行的盈利来源和核心竞争力。     

Modeling the business risk of financially weakened firms: A new approach for corporate bond pricing

Most structural models of default risk assume that the firm's asset return is normally distributed, with a constant volatility. By contrast, this article details the properties that the process of assets should have in the case of financially weakened firms. It points out that jump-diffusion processes with time-varying volatility provide a refined and accurate perspective on the business risk dimension of default risk. Representative Arrow-Debreu state price densities (SPD) and term structures of credit spreads are then explored. The credit curves show that the business uncertainties play a major in the pricing of corporate liabilities.     

Optimal portfolios when volatility can jump

We consider an asset allocation problem in a continuous-time model with stochastic volatility and jumps in both the asset price and its volatility. First, we derive the optimal portfolio for an investor with constant relative risk aversion. The demand for jump risk includes a hedging component, which is not present in models without volatility jumps. We further show that the introduction of derivative contracts can have substantial economic value. We also analyze the distribution of terminal wealth for an investor who uses the wrong model, either by ignoring volatility jumps or by falsely including such jumps, or who is subject to estimation risk. Whenever a model different from the true one is used, the terminal wealth distribution exhibits fatter tails and (in some cases) significant default risk.     

Subprime Loan Default Resolutions: Do They Vary Across Mortgage Products and Borrower Demographic Groups?

This paper examines default outcomes for subprime first lien loans during the recent subprime mortgage boom. It conducts this investigation in two phases. The paper first examines factors associated with pre-foreclosure outcomes for subprime mortgages in default. It then examines factors associated with different outcomes for loans that enter foreclosure. These factors include less understood elements such as mortgage product features and borrower demographics. The analysis is based on detailed loan-level data and employs multinomial logit models in a hazard framework. Results show that default resolutions vary with product features and borrower demographics. Adjustable rate and interest-only mortgages, and loans with low- or no-documentation are more likely to enter foreclosure proceedings, and, once in foreclosure, are more likely to become REO. The existence of junior liens increases the probability of the loan remaining in default. Owner-occupancy is associated with lower likelihood of foreclosure initiation and REO, and greater likelihood of curing default. Additionally, default outcomes are impacted by local legal, economic and housing market conditions, and the equity in the home.