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.     

A theory of predictable excess returns in real estate

A principal-agent model is employed to characterize the equilibrium mortgage contract. The value of a house depends on the actions of its owner but affects the wealth of both the owner and the lender who writes the mortgage contract with which the house is purchased. Because of this, the buyer is exposed to moral hazard. In some situations, this can lead to inefficient maintenance and predictable excess returns to home ownership. Even though there are potential buyers willing to pay back more money, the bank will not write loans for these consumers because of the adverse incentive effects of such an action.     

Comparing Present Value Cost Differentials between Fixed- and Adjustable-Rate Loans: A Mortgage Simulation

When a borrower chooses between a fixed-rate and an adjustable-rate loan, he is doing so based on expectations of future interest rates and the expected life of the loan. This paper demonstrates how Monte Carlo simulation can be employed to assist in decision making when the borrower is confronted with the choice of fixed or adjustable-rate mortgages. Present value costs of future mortgage payments are modeled using actual lending parameters offered over a 50-month period, at varying borrower discount rates, and with different mortgage holding periods. The selection of a fixed-rate or a variable-rate mortgage is shown to be sensitive to mortgagee holding period and discount rates as well as to market conditions.     

Valuing mortgage loan servicing

We develop an intertemporal model for valuing mortgage loan servicing contracts. The model includes a stochastic short-term interest rate and realized inflation rate which jointly determine the current mortgage coupon rate, the mortgagor's prepayment decision, the servicer's future net cash flows, and the rate at which to discount these future cash flows. Several potential uses of the model for institutions that service mortgages and trade servicing portfolios are illustrated by the application of the model to servicing fixed-rate mortgages and adjustable-rate mortgages. The model also is applicable to regulatory issues and to the servicing of other types of loans.The authors gratefully acknowledge support from the Federal Home Loan Bank Board, Washington, D.C., the Purdue Research Foundation, West Lafayette, Indiana, and the Richard D. Irwin Foundation, Homewood, Illinois.     

Hedging individual mortgage risk

This paper investigates the feasibility of an individual hedging the interest rate risk involved in planning to take out a mortgage at a future point in time. Simulation using market data indicates that a simple futures hedge reduces the variation in mortgage capacity by about one half. Expected mortgage capacity is very close to 100% of the original capacity at a very low cost. Hedging the individual mortgage with a put futures option is less effective in reducing downside risk and has a higher expected cost.     

Renegotiation in the Common Law Mortgage and the Impact of Equitable Redemption

This paper seeks to fill a gap in the real estate finance literature by linking the well-known history of the Anglo–American mortgage recorded by legal scholars with the recent literature on security design and incomplete contracting in order to explain and evaluate several unique features of the mortgage. In particular, we investigate how a conditional transfer of ownership to a lender and the institution called the equity of redemption affect mortgage renegotiation and therefore the value of mortgaged real estate. Given the governance of the common law mortgage, we show that a mortgagor may not be able to renegotiate his mortgage debt in order delay repayment when faced with a re-investment opportunity during the life of the mortgage. The failure to optimally renegotiate the mortgage does not necessarily result in foreclosure but may result in underinvestment. Therefore, an additional period of time between default and foreclosure, known as a period of equitable redemption, may allow the mortgagor to accrue sufficient cash flow to not only avoid foreclosure but to mitigate underinvestment in non-default states. Since this extra period of time may not be achievable ex post due to a hold-up problem, its inclusion ex ante may be welfare improving.     

Discount Point Concessions and the Value of Homes with Conventional versus Nonconventional Mortgage Financing

This is an empirical investigation on the impacts of certain seller concessions on home prices. Specifically, we examine the impacts of two seller concessions: discount point concessions (DPCs) and closing cost concessions (CCCs) on home prices. Using hedonic analysis, we find that DPCs are capitalized into home prices. We do not find that CCCs produce capitalization effects. DPCs appear to work in a manner similar to other creative financing techniques such as a buydown mortgage. DPCs enhance affordability by lowering interest costs and debt service payments. DPCs thus lead to increases in effective demand. CCCs will reduce out of pocket expenses but will not necessarily enhance long-term affordability, thus their price effects are less certain. We show that these price premiums are prevalent only when conventional mortgage financing is used. When FHA and VA loans are used, premiums disappear. Of course, governmental insured/guaranteed loans are much more subject to regulation than conventional loans, which may prevent homesellers from price premium maximization. The study establishes the relative significance of discount points versus closing costs as marketing incentives. It appears that the use of discount points as a marketing incentive produces more capitalization effects. The presence of such capitalization effects is consistent with results found in other creative financing studies.     

Rational Prepayments and the Valuation of Collateralized Mortgage Obligations

This article presents a procedure for evaluating collateralized mortgage obligation (CMO) tranches. The solution procedure is in the spirit of a dynamic programming problem in which an individual mortgagor's decision to prepay is the feedback control variable―the mortgagor seeks to minimize the value of the mortgage subject to refinancing costs. We employ a two-step procedure to solve this dynamic programming problem. The first step uses an implicit finite difference backward solution procedure to determine the “optimal” prepayment boundary for a class of mortgagors, each of whom confronts the same proportional refinancing cost. This step is repeated for several different classes of mortgagors that differ in the level of refinancing costs that they confront. The outcome of this first step is a series of prepayment boundaries―one set of boundaries for each level of refinancing costs (i.e., one set of boundaries for each refinancing cost category of mortgagors). In the second step, the prepayment boundaries determined in the first step are used in conjunction with Monte Carlo simulation to value the CMO tranches. The essence of the second step is that when the simulated interest rate hits the boundary for a particular class, it triggers a prepayment scenario for that class of mortgagors. We conduct extensive sensitivity analysis to determine the robustness of this approach (and our solution procedure) to alternative single-factor models of the term structure of interest rates and to alternative specifications of the distribution of refinancing cost levels confronted by mortgagors. The sensitivity analysis indicates that CMO tranche valuation is not particularly sensitive to alternative models of the term structure so long as the models are consistent with the current yield curve, but, even when alternative specifications of the refinancing cost categories generate nearly identical values for the collateral underlying the CMO (i.e., the generic mortgage-backed securities), the resulting tranche values can differ widely between the two specifications. The results point out the importance of accurate estimation of the distribution of refinancing costs when the rational valuation model is used for the analysis of CMO tranches.     

Originators,wholesalers, and conduits: The marginal value of the contract rate on 30-year conventional mortgages

The model we present solves for the value of an incremental change in the mortgage contract given an expectation about the time the mortgage will be outstanding and a required return for this time span. The marginal value participants in the primary mortgage market place on the contract rate of a 30-year conventional mortgage determines the array of bids for new mortgage production. Mortgagors can issue mortgages at various discounts. High discounts are associated with low contract rates, and low discounts are associated with high contract rates. This article examines the way wholesale dealers and conduits value the various contract rates associated with current production of 30-year conventional mortgages.     

Current Wealth,Housing Purchase,and Private Housing Loan Demand in Japan

Japanese households accumulate wealth for down payments at a high rate. Therefore, current wealth plays an important role in home acquisition as well as public loans whose direct mortgage lending is a strong support for home purchasers. We estimate the wealth effect on private mortgage debt as well as housing consumption by applying a model where mortgage-debt demand is derived from house-purchase decisions and is determined jointly with housing consumption. We use a simultaneous equation Tobit estimation method. Wealth effects on private mortgage debt, likelihood of borrowing, and housing consumption are not elastic. On the other hand, a change in housing consumption affects the likelihood of borrowing elastically much more than the private mortgage amount of borrowers. Housing and private mortgage markets fluctuate very closely with the number of participants in the mortgage market. Therefore, the number of housing starts is linked strongly to the private mortgage market.     

Wealth Distribution, Inflation Tax, and Societal Benefits of Illiquid Bonds

Illiquid nominal government bonds are shown to have two opposing effects on welfare. First, the relatively poor choose to top-up money balances for future consumption by purchasing nominal bonds at a discount. The wealth distribution becomes more centered with a smaller consumption deviation from the first best. Second, the higher inflation tax on monetary wealth to finance interest payments makes money less valuable, so that the quantity of output produced in exchange for money decreases. The trade-off between the welfare-enhancing effect on wealth distribution and the distortionary effect on output implies the socially optimal discount rate and liquidity.     

The refinancing threshold pricing model: An economic approach to valuing MBS

Investigation of MBS prepayment data indicates that mortgagors have different interest rate levels, or thresholds, at which they exercise their option to prepay their mortgage. In order to properly value an MBS with heterogeneous mortgagors, Merrill Lynch has developed the Refinancing Threshold Pricing Model (RTP). The RTP model focuses on the refinancing decision of the mortgagor when pricing the mortgage pool. The model divides each pool into groups of mortgagors who share similar refinancing costs. Using market data, the RTP model endogenously determines both the implied costs that mortgagors face, as well as the proportion of the MBS pool in each refinancing cost group. In addition to determining pool value, the RTP model also calculates MBS duration, dP/dY and convexity. Comparison between RTP model values and actual market data reveals a strong correlation. The RTP has a wide range of applications, including valuing 15-year and 30-year conventional MBS; pricing interest-only (IO)/principal-only (PO) derivative MBS; determining new versus seasoned MBS price spreads; and valuing specific MBS pools.The information set forth was obtained from sources we believe reliable, but we do not guarantee its accuracy. Neither the information, nor any opinion expressed constitutes a solicitation by us for the purchase or sale of any securities or commodities. Merrill Lynch, Pierce, Fenner & Smith, Inc. or its affiliates may have either a long or short position in, and may buy and sell for its own account or the accounts of others, these securities.     

浮动利率房贷提前还款的损失度量

住房抵押贷款是银行一项重要业务和资产.随着利率的波动和其他因素的影响,借款人有可能提前还款从而影响银行的收益.准确地度量提前还款给银行带来的损失有助于商业银行更好地管理这类经营风险.在具有均值回复特性的随机市场利率和服从纯跳跃过程的浮动住房贷款利率条件下,以最常见的每月等本金还款方式为基础,根据对利率的预测,使用求期望的办法估算出银行房贷总收益的预期值,然后将该预期值折现到提前还款发生时刻,从而构造出借款人在合同期间提前偿还房贷给银行造成的利息损失度量模型.     

The valuation at origination of fixed-rate mortgages with default and prepayment

This paper develops a model to rationally price fixed-rate mortgages, using the arbitrage principles of option pricing theory. The paper incorporates amortization, prepayment and default in valuing the mortgage. Having completely specified the model, numerical procedures value the different features of the mortgage contract under a variety of economic conditions. The necessity of having both the interest rate and the house price as explanatory variables, due to the interaction of default and prepayment, is demonstrated. The numerical solutions presented center around mortgage pricing at origination. Thus, variations in the equilibrium contract rate are examined for differing economic conditions and changes in the contract. Finally, by presenting a complete model, the paper yields insights for the existence of common institutional practices.     

Discounting Mean Reverting Cash Flows with the Capital Asset Pricing Model

Discounting cash flows requires an equilibrium model to determine the cost of capital. The CAPM of Sharpe and the intertemporal asset pricing model of Merton (1973) offer a theoretical justification for discounting at a constant risk adjusted rate. Two problems arise with this application. First, for mean reverting cash flows the risk adjustment is unknown, and second, if the present value is compounded forward then the distribution of future wealth is likely right skewed. I develop equilibrium discount rates for cash flows whose level or growth rate is mean reverting. Serial correlation also largely eliminates the skewness problem.     

Quantifying time value errors

Time valuation of cash flows is an essential part of personal financial planning and management. Many financial arrangements are priced according to a cash-flow valuation model. Expected cash flows associated with a stock or bond are discounted at an appropriate risk-adjusted rate in order to determine the fair value of the financial asset. Home mortgage loans are priced according to the discounted value of the future principal and interest cash flows. Yet, despite the importance of the discounted cash flow methodology in pricing assets, computational errors are often made when discount factors are not calculated precisely. This article attempts to quantify the magnitude of the error when the mathematical function for present value is ignored and interpolation is used instead to determine the discount factor.     

CEO Risk‐Taking Incentives and the Cost of Equity Capital

In this paper, we show that the sensitivities of an executive's wealth to changes in stock prices (deltas) decrease the implied cost of equity capital while the sensitivities of an executive's wealth to changes in stock volatility (vegas) increase the implied cost of equity capital. Our findings demonstrate that shareholders understand the risks of firms’ future projects as embedded in executive compensation and price these risks into the cost of equity capital accordingly. The findings have strong implications for optimal executive compensation contract design, project evaluation and cost of capital estimation.     

The change in information uncertainty and acquirer wealth losses

A large body of literature demonstrates that acquisitions are on average value destroying for the acquirer. We investigate whether the change in the acquirer??s information uncertainty contributes to acquirer wealth losses. Information uncertainty affects the discount rate (the cost of capital), which in turn influences stock price. Our results indicate that acquisitions lead to increases in information uncertainty, as proxied by analysts?? earnings forecast dispersion. We also find that the change in information uncertainty is negatively related to acquirer long-term stock performance, after controlling for the acquirer??s fundamentals. Taken together, this evidence is consistent with the conclusion that increases in information uncertainty resulting from acquisitions contribute to acquirer post-acquisition wealth losses     

Price Elasticity of Demand and an Optimal Cash Discount Rate in Credit Policy

While the provision of a cash discount is equivalent to a reduction in price, the role of price elasticity of demand in determining credit terms has been neglected in the extant literature. In this paper, this role is investigated and it is shown that the optimal cash discount rate is affected by the price elasticity of demand for the firm's product. The comparative effects on the optimal cash discount rate with respect to exogenous changes in the fraction of credit sales paid after taking cash discount, the cost of short-term funds and the bad debt loss ratio are investigated. A trade-off between the time value gain and the price elasticity of demand is established. We find that firms which sell in locations having different price elasticities for their products, and/or which face various costs of short-term funds in different locations, should vary their cash discount terms accordingly.     

Accounting for Risk and Return in Equity Valuation

Standard valuation models forecast cash flows or earnings, add a growth rate, and discount the cash flows to their present value with a discount rate that typically reflects the cost of capital. But as the author argues, projecting the long‐term growth rate is essentially speculative; and along with uncertainty about the growth rate, analysts generally do not have a good grasp of the discount rate either. Thus, instead of reducing uncertainty, these two features effectively compound uncertainty in valuations in the sense that slight changes in the growth rate or discount rate can change the valuation considerably. In this article, the author proposes an alternative approach that views the investor's problem as one of challenging the speculations that are built into the current market price, particularly the speculation about growth. Rather than building in a speculative growth rate (and thereby treating it as if it were a certainty), the author's approach turns the problem on its head by using an accounting analysis of the firm's current earnings and cash flows that provides a basis for recognizing the speculative component of the current stock price. More specifically, the author's analysis identifies the future earnings growth path that is implied by the market price, which can then be evaluated with the question: Do I want to pay for this growth? Because growth expectations are risky, additional analysis can be used to provide an understanding of the risk and return to buying growth, and of the upside and downside if risk growth expectations are not realized. By taking such an approach, investors incorporate their understanding of risk not by increasing the discount rate, but by recognizing that the primary risk in investing is the risk of overpaying for growth.