The Performance of Commercial Mortgages

This study examines the return characteristics of a large, well-diversified commercial mortgage portfolio. Mortgage-specific cash-flow histories are constructed for 2,480 loans originated over the period 1974 through 1990, and a contingent-claims approach to pricing risky debt is used to estimate inter-temporal market values. Quarterly holding-period returns are compared across selected mortgage groups and to alternate asset classes. Our findings suggest that both mortgage returns and volatility of return are comparable to those of other forms of fixed-income assets over the study period. Implied property price volatility is found to average 17%, a result significantly higher than reported in earlier studies. While mortgage returns are found to vary by property type and region of origin, cross correlation of returns is found to be high, illustrating the systematic effect of interest rates on the performance of commercial mortgages over the period 1974 through 1990. However, an increase in credit risk in the latter years of the study suggests that diversification may be a worthwhile objective for holders of these assets. We do not find evidence to suggest that abnormal returns were earned on commercial mortgage portfolios over the study period.     

Valuing the Mortgage Borrower's Prepayment Option

This paper investigates the value of the prepayment option that normally accompanies a fixed-rate mortgage. Using the two-state option-pricing model developed by Bartter and Rendleman, the paper presents simulations of prepayment option values using several sets of interest rate parameters. The sensitivity of the value of the option to changes in various aspects of the mortgage contract is assessed. Prepayments are not priced separately in the market from the underlying mortgage, so the paper investigates how the inclusion of a prepayment option affects the contract interest rate. Finally, there is reason to believe that any option-pricing model will overestimate the value of a mortgage prepayment option. The size of this bias is assessed indirectly and is found to be rather small.     

Determinants of Credit Spreads in Commercial Mortgages

This article examines the cross-sectional and time-series determinants of commercial mortgage credit spreads as well as the terms of the mortgages. Consistent with theory, our empirical evidence indicates that mortgages on property types that tend to be riskier and have greater investment flexibility exhibit higher spreads. The relationship between the loan-to-value (LTV) ratio and spreads is relatively weak, which is probably due to the endogeneity of the LTV choice. However, the average LTV ratio per lender has a strong positive relation with credit spreads, which is consistent with the idea that lenders specialize in mortgages with either high or low levels of risk, and that high LTV mortgages require substantially higher spreads. Finally, we observe that spreads widen and mortgage terms become stricter after periods of poor performance of the real estate markets and after periods of greater default rates of outstanding real estate loans.     

Valuing the Redevelopment Option Component of Urban Land Values

This study draws from the redevelopment, real option, and urban spatial growth literatures to explore the spatial dynamics of the components of house prices. More specifically, the paper proposes that the capitalized value of the option to redevelop housing at the property level can be estimated by incorporating the likelihood of exercising the redevelopment option (the probability of redevelopment) into spatial and nonspatial hedonic house price models. Accordingly, option values are estimated for properties across the spectrum of the housing life cycle. Results from the study reveal a substantial level of spatial variation and clustering in the predicted option values, indicating that location is a major determinant of redevelopment and real option values. Furthermore, the results provide new evidence in support of the theoretical construct that properties purchased for immediate redevelopment are only valued for the underlying land.     

ARM Wrestling: Valuing Adjustable Rate Mortgages Indexed to the Eleventh District Cost of Funds

This article analyzes adjustable rate mortgages (ARMs) based on the Eleventh District Cost of Funds Index (EDCOFI). The behavior of EDCOFI was examined over the period 1981–1993. Adjustments in this index lag substantially behind term structure fluctuations. Also, the seasonality and days-in-the-month effects noted by previous authors are really symptoms of a January effect . A finite difference valuation algorithm was developed which accounts for all usual ARM contractual features, in addition to the dynamics of EDCOFI. This pricing algorithm allows us to determine endogenously the optimal prepayment strategy for mortgage holders, and hence the value of their prepayment options. The dynamics of EDCOFI give significant value to this option, typically around 0.5% of the remaining principal on the loan.     

Pricing Default Risk in Mortgages

This paper examines the valuation of fixed-rate mortgages and the pricing of insurance against default on such mortgages. Both the mortgage and the insurance are treated as compound European put options. A put is the right, but not the obligation, to turn over an asset to another party for a specified payment, and being a European put indicates that this can only occur at a specified expiration date. The mortgage contract, and hence the insurance on it, fit into a European option framework because no rational borrower would ever choose to default until a payment is due. Mortgages are compound options in nature because at each payment data prior to the last one, the borrower either defaults or purchases a new option to default at the next payment date by making the scheduled payment. Since the current value of the mortgage is affected by options to default in the future, the problem is solved working backwards in time with the value of later options feeding into the earlier ones, so that the process builds on itself in a recursive fashion. Using familiar arguments from option-pricing theory, the value of any of the assets in the model is expressed as the solution to a partial differential equation, where the terms of the contract yield the appropriate terminal conditions. Standard numerical procedures are then used to produce the value of the mortgage and the insurance under various economic conditions. The simulations indicate that the prime determinants of the value of the assets considered are the volatility of the house price and the volatility of the spot interest rate. Sensitivity tests show that changing either of these parameters affects the results substantially more than any of the other parameters examined. The paper completely analyzes the default option and insurance against default on the mortgage. It is one part of a complete model of fixed-rate mortgages that would allow for both prepayment and default and treat the interaction of the two options. The general approach outlined in this paper can be used to develop such a model as well as to value any mortgage-related security. In light of the increasing variety and the complexity of such instruments in the market today, the presentation of our approach to these valuation problems is perhaps the most important contribution of the paper.     

商业地产投资的实物期权特性及应用框架研究

商业地产开发投资中存在投资的不可逆性、外部环境的不确定性和决策的灵活性,因而具有实物期权特性。从确定要解决的问题、分析不确定性的来源、鉴别关键的不确定性因素、识别实物期权类型、构建期权定价模型、计算项目价值、检查计算结果和重新设计8个方面,构建了商业地产投资决策的实物期权分析框架。     

On the Design and Pareto-Optimality of Participating Mortgages

This paper develops a micro-economic model and proceeds with numerical simulation to demonstrate that participating mortgages can improve social welfare when the real estate ownership is shared among the different taxable entities. The optimal distribution of real estate ownership and lending will tend to be concentrated in taxable and nontaxable hands, respectively, with lending conducted via participating mortgages. This paper also demonstrates the violation of the well-known, risk-neutral valuation argument of the Black and Scholes (1973) model because of the lack of a riskless hedge due to the uniqueness of real estate.     

Reverse Mortgages and the Liquidity of Housing Wealth

Housing wealth constitutes most of the non-pension wealth of the elderly population. This study analyzes the potential of reverse mortgages to increase the income and liquid wealth of the elderly by identifying households with relatively high levels of housing equity. Because this article looks at the whole distribution of elderly households and considers debt as well as income, it finds a larger potential market for reverse mortgages than previous studies.
Calculations from the 1990 Survey of Income and Program Participation and Census population estimates show that over six million homeowners in the United States could increase their effective monthly income by at least 20% by using a reverse mortgage. Of these, more than 1.3 million have no children. Furthermore, a reverse mortgage would allow over 1.4 million poor elderly persons to raise their incomes above the poverty line.     

Correlation Dynamics and Determinants in International Securitized Real Estate Markets

We find the correlation movements among eight developed securitized real estate markets and among their stock markets are quite synchronized over the period from 1995 through 2012. There is a high degree of correlation dependence with many of the realized correlation series subject to regime switching. Moreover, international correlations of public property returns could be significantly explained by five real estate variables that include global real estate securities market volatility, co‐existence of real estate investment trust (REIT) influence, underlying direct real estate return performance differential, real estate securities volatility differential and real estate securities market size differential after controlling for macroeconomic influence and stock market effect. The importance of the control and real estate variables in explaining the return correlations varies across the economies examined.     

Interest-Rate Volatility, Basis Risk and Heteroscedasticity in Hedging Mortgages

This paper investigates the validity of the OLS regression to estimate the hedge ratio for mortgages (GNMA) and provides alternative methodologies. In particular, this paper is concerned with the variance structure (conditional and unconditional heteroscedasticities) and the misspecification (nonlinearities) of the simple linear regression model for direct as well as cross-hedging. Using data on spot prices of GNMA and futures prices of GNMAs and T-bills for the period September 1979 to January 1985, we show that there exists significant heteroscedasticity particularly for cross-hedging, and nonlinearity between cash and futures prices for direct as well as cross-hedging. Alternative hedge ratio estimates are provided using the Box-Cox transformation model and an autoregressive conditional heteroscedastic (ARCH) Model.     

Mortgage Loan Characteristics,Unobserved Heterogeneity and the Performance of United Kingdom Securitized Subprime Loans

We estimate a competing risk model of mortgage terminations on samples of U.K. securitized subprime mortgages. Given the role of these loans in the recent financial crisis it is important to understand their performance and supposed idiosyncratic behavior. We use a flexible modelling of unobserved heterogeneity over several dimensions, controlling for selection issues involving initial mortgage choices and dynamic selection over time. We estimate the characteristics of the unobserved heterogeneity and determine the correlation between the unobserved components of default and prepayment. The paper demonstrates the need to estimate initial household choices and the durations to default or prepayment jointly.     

Parameter Stability and the Valuation of Mortgages and Mortgage‐Backed Securities

The recent financial crisis was triggered by large and unexpected losses on mortgages and mortgage‐related securities. Here we examine model risk arising from innovations in mortgage markets and the effect on asset values. In particular, we examine the effect of parameter instability in the prepayment function. Using carefully constructed microdata, we find that the refinancing propensity was greater in 1998 for a 1997 issue given the same incentives, compared to the 1993 performance of a 1992 issue. The associated change in cash flow patterns produces economically significant changes in asset prices. Results are robust to alternative term structure models.     

The Borrower's Choice of Fixed and Adjustable Rate Mortgages in the Presence of Nominal and Real Shocks

This paper concerns the conditions under which borrowers select fixed and adjustable rate mortgages. The novelty of the paper lies in its capability to analyze the effect of nominal and real shocks separately. The fixed rate mortgage (FRM) versus the adjustable rate mortgage (ARM) choice is determined by the expected real interest rate differential, initial wealth, income, expected real and nominal income risk exposure—measured by different parameters—the value of the house, the appreciation of the house and the influence of the variance of nominal and real shocks. Results differ according to whether or not borrowers are restricted by the loan-to-value constraint.     

Inflation Risk, Payment Tilt, and the Design of Partially Indexed Affordable Mortgages

This paper integrates two fundamentally important parameters into a theory of optimal mortgage design: the proportion of inflation risk borne by the lender / investor and the borrower and the amortization-graduation schedule for loan repayments. Equations are derived for a family of innovative mortgages, termed hybrid PLAMs, which offer advantages to borrowers and lenders over either the standard fixed rate mortgage (FRM) or the price level adjusted mortgage (PLAM). The superiority of the hybrid PLAMs lies in their ability to simultaneously and independently accommodate differing degrees of inflation-risk sharing and payment affordability. Inflation-risk sharing is represented by an indexation parameter set over a continuum of values such that the FRM has zero index variability and the PLAM has unit index variability. Similarly, payment tilt is represented by a tilt parameter such that the FRM has zero tilt and the PLAM has unit tilt. We demonstrate that these two parameters are independent and can each be continuously varied in a two-dimensional family of self-amortizing mortgages. A specific hybrid PLAM can be designed to partition inflation risk in any proportion between the borrower and the lender and to simultaneously prescribe any level of payment tilt between the extremes of the FRM and PLAM. The behavior of representative hybrid PLAMs is simulated and compared to FRMs and PLAMs for three different inflation scenarios, one of which uses actual market data from the period of 1960–1990.     

The Impact of Interstate Foreclosure Cost Differences and the Value of Mortgages on Default Rates

Previous research on mortgage default has focused on the costs, benefits, and characteristics of the mortgagor. In such studies default rates have been taken as a measure of mortgage risk. In this paper we present a model where the position of the lender affects the default-foreclosure process. Important to the lender's decision to foreclose rather than renegotiate an existing loan are the value of mortgage and the legal costs associated with foreclosure.
The empirical evidence supports the hypothesis that both the value of the mortgage and legal foreclosure costs affect the foreclosure rate. In those states where legal foreclosure costs are high rates are significantly less than where costs are low. This suggests that previous models which include only the costs and benefits of default to the borrower are incomplete and that foreclosure rates can not be taken as a strict measure of mortgage risk. That is, low foreclosure rates may indicate that losses occur in other forms of loan negotiation rather than in expensive legal costs.     

Mixed Uses and the Redevelopment Option

This paper considers how the potential for mixing uses and redevelopment impact property value. Operating flexibility of this type is found to significantly increase property value when the correlation between payouts from different property types is low or when redevelopment costs are low. The ability to mix uses and redevelop over time is also shown to affect the timing of initial land development. The shape of the development boundary is shown to differ considerably depending on whether marginal revenue is constant or decreasing to scale. Both policy and empirical implications concerning the effects of multiple-use zoning are discussed.