.. 

A Choice-Theoretic Model of Single-Family Mortgage Default 

Peter J. Elmer 

Senior Economist 

Federal Deposit Insurance Corporation 

Division of Research and Statistics 

550 17th St., N.W. 

Washington, D.C. 20429 

Phone:202-898-7366 

Fax:202-898-7222 

e-mail: pelmer@fdic.gov 

FDIC Working Paper 

97-1 

Abstract: A choice-theoretic model of single-family mortgage default has been developed in 

environments in which put option models do not apply. Such environments can be found in the 

many jurisdictions and economic settings that have no legal foundation for asserting the rights 

associated with a put option. The model specifies a consumer choice framework for analyzing 

mortgage default that recognizes income-related variables, trigger events, and insolvency. The 

model suggests that default is primarily due to borrower insolvency, which is motivated by 

negative shocks to income and house prices, but not to interest rates. Empirical implications of 

the model are consistent with many observed characteristics of mortgage default that are 

inconsistent with, or otherwise difficult to explain by, option-based models. 

I would like to thank Steve Seelig, Charles Capone, Dave Ling, Pat Hendershott, Tom Reeves, 

Claire McGuire, Jody Harrington, Tom Feeney, Barbara Sarshik, Tom Holzman, Anton 

Haidorfer, Jim Wallace, Wayne Passmore, and Joseph Rinaldi for helpful comments. The views 

expressed are those of the author and not necessarily those of the Federal Deposit Insurance 

Corporation. 
.. 

I. Introduction 

During the past decade it has become commonplace to view single-family mortgage 

default as a put option according homeowners the right to demand that lenders purchase their 

home in exchange for mortgage elimination.1 In many settings, however, a variety of issues serve 

to question this view of mortgage default. 

Put option models have no legal foundation in many jurisdictions. Standard promissory 

notes confer personal liability on borrowers and permit lenders "recourse" to seek to recover 

default-related losses. Deficiency judgments and other legal remedies, though sharply limited in 

some jurisdictions, are clearly permitted in many others. Moreover, legal information and risk are 

subject to asymmetries because lenders generally have far more expertise and resources for 

dealing with default than delinquent borrowers do. These factors, along with choice-theoretic 

issues, point to a need for alternative models. 

Consumer theory traditionally ascribes a central role to borrower income, savings, and 

other forms of wealth, yet put option models reserve no role for these variables. Theory normally 

posits that various forms of personal wealth are fungible, which precludes separation of 

homeowner equity from other assets when describing consumer actions. In contrast, put option 

models treat home equity as separable from other borrower assets. Hence, they take mortgage 

default to be independent of insolvency and default on other obligations.2 

A variety of empirical regularities also point to the need for a broader framework. 

Unsecured borrowing and savings patterns along with personal credit ratings have been shown to 

play a role in mortgage default.3 Although tests generally confirm the importance of homeowner 

equity, they also find that other variables, such as borrower income and mortgage type, help 

2 
. 

explain mortgage default.4 Similarly, rating agencies tend to place borrower credit risk, mortgage 

type, and other variables alongside real estate equity in their models of mortgage default. 5 

This paper develops a choice-theoretic model of single-family mortgage default. In an 

effort to make the model broadly applicable, the topic of personal bankruptcy is deferred to 

another discussion. Note too, that for the most part, the exhaustion of borrower wealth is 

considered to be synonymous with insolvency. 

The paper is organized as follows: Section II examines legal issues that necessitate 

alternative models and the environments in which they should be considered. Section III presents 

a choice-theoretic model of mortgage default applicable in these environments and consistent 

with standard elements of consumer theory. Section IV applies the model to identify fundamental 

determinants of default. Section V extends the analysis to explore the interaction of the primary 

sources of risk. Section VI discusses empirical implications of the choice-theoretic model. 

Section VII summarizes the results and conclusions. 

II. Legal Issues 

In many jurisdictions treating mortgage default as a put option is inconsistent with five 

aspects of mortgage law.6 First, standard promissory notes promulgated by the Federal Home 

Loan Mortgage Corporation (FHLMC) and the Federal National Mortgage Association (FNMA) 

require each person signing the notes to be "fully and personally obligated to keep all of the 

promises" of the note. Personal liability has legal as well as financial dimensions. Legally, 

personal liability links mortgage liability to other borrower assets and liabilities, thereby enabling 

mortgage creditors to place claims on other forms of borrower wealth in the event of default. 

3 
. 

Financially, personal liability distinguishes homeowner equity in real estate from ownership of 

corporate equity which is characterized by limited liability. In this regard, Merton's, ( 1973) 

insight that corporate equity, may be viewed as a put option, which is justified by the limited 

liability of corporate equity, does not apply to the personal liability of home equity. 

Second, standard contractual terms do not support the rights associated with a put option. 

Although standard FHLMC-FNMA contracts grant borrowers an option to prepay or "call" a 

mortgage prior to maturity, they also grant lenders the right to demand payment of all 

outstanding principal and interest and to be reimbursed for reasonable costs, fees, and expenses 

incurred in enforcing the note, such as attorney's fees. Furthermore, borrowers waive certain 

rights to demand that the lender perform certain acts, such as "accelerating" payment of amounts 

due upon default. In general, borrowers contract an obligation to honor the debt, whereas lenders 

contract the right, but not the obligation, to pursue foreclosure. To the extent that borrowers have 

an "option" to default, exercising the option constitutes a breach of the standard note and 

mortgage contracts that may impart personal liability for damages to the borrower. 

Third, lenders have at least limited rights to pursue deficiency judgments or other legal 

remedies for recovering default-related losses, although the procedures vary considerably from 

one jurisdiction to another.7 States with ''judicial foreclosure" permit deficiency judgments at the 

time of foreclosure, whereas "nonjudicial foreclosure" states require separate legal action. Other 

legal exigencies might also apply, such as strict notice requirements and time limits, rights of 

redemption, and rules requiring that the "fair market value" of the property be used as the basis 

for the deficiency. Several states either formally prohibit deficiency judgments on residential real 

estate or maintain an antideficiency environment in some other manner. 8 Whatever the 

4 
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jurisdictional and legal issues, most states permit some form of deficiency pursuit, as can be seen 

in corporate policies on deficiency judgments at national mortgage intermediaries, such as 

FHLMC and FNMA, and among numerous private sector agents specializing in collection.9 

The fourth point is that home equity cannot be separated from other borrower assets and 

liabilities. Borrowers can contract second or other subordinated debts that impair home equity in 

a fashion similar to the first-mortgage liability: for example, subordinated claims must be paid at 

a voluntary sale and they possess acceleration right in the event of default. Also, liens on the 

borrower's home may be attached by a variety of other creditors, such as suppliers of labor or 

materials and taxing authorities. Most states provide unsecured creditors with the right to obtain 

"judgment liens" for other types of claims, which become liens against all debtor real estate of 

the county in which docketing or recording occurs. 10 Given that the location of a debtor's 

residence is normally well known to creditors, it is a convenient target for claims. 11 

Fifth, the foregoing points are reinforced by asymmetries in legal information and risk. 

Most lenders have extensive legal expertise and procedures for dealing with delinquent 

borrowers and with the legal requirements of each jurisdiction. In addition, home mortgages 

create personal liability for borrowers and otherwise favor the lender's position. Few borrowers 

can match this legal expertise and knowledge of jurisdictional foreclosure requirements or find 

grounds for asserting limits on their liability. Such a one-sided relationship may leave borrowers 

with little hope of winning disputes over liability, even in jurisdictions with pervasive antideficiency environments. 

Figure 1 illustrates several legal issues that arise when mortgage default is treated as a put 

option. Assume that the borrower possesses home equity whose value is determined by variable 

5 
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house prices (p') coupled with a fixed mortgage (m) and fixed interest rate (i). That is, equity 

equals p 1 

- m(l +i). Other wealth is the interest used to service the mortgage debt mi plus an 

arbitrary constant (k). The solid line shows first-mortgage default treated as a put option. This is 

a standard put option payoff schedule rising dollar for dollar as house prices fall below mortgage 

values. 12 Default occurs only to the left of A, with the result that wealth increases along AB. 

This option payoff applies when no subordinated claims exist and in jurisdictions with pervasive 

anti-deficiency environments. In other jurisdictions, the cost of a deficiency judgment is 

approximated as the difference between mortgage liability and house price, so put values along 

AB imply deficiencies in the shaded region ABC, which is bounded by k wealth. The cost or risk 

of a deficiency judgment thereby equals the economic benefit of the put option as long as k is 

available to support the judgment. A subordinated claim (s) shifts the put payoff from AB to DE. 

In this case, the judgment region undergoes a similar shift, from ABC to DEF. No put payoff 

applies to borrowers who perceive a very low probability of prevailing over lenders in liability 

disputes. 

Several attempts have been made to address the legal issues just described. It has been 

agrued for example, that prohibitions and costs associated with the collection of deficiencies 

render personal liability valueless (Jones (1993)). This suggestion directly applies to the handful 

of states with predominantly anti-deficiency environments. However, it carries less weight as the 

strength of the anti-deficiency environment declines owing to the presumption of lender legal 

expertise. Even if pursuit imposes additional notice requirements or bidding procedures, lender 

6 
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m(l+i,n)- p' 

( option payoff) 

k 

mi 

C 

m-k 

Figure 1 

Mortgage Default Option Payoff 

A F 

m(l+i) m-k+s 

7 

. . . 

. 

. . . . 

D 

m(l+i)+s 

p' 
. 

legal advisers can be expected to be aware of these requirements and capable of meeting them. 

More important, many states clearly permit the pursuit of deficiency judgments, so personal 

liability is expected to have value in these jurisdictions. 

It has also been pointed out that some lenders do not, as a matter of policy, pursue 

deficiency judgments. The Federal Housing Authority for one, has supported such a policy for 

many years (Jones, 1993). To the extent that borrowers are aware of such a policy and confident 

of its enforcement, personal liability again becomes valueless, and put option models can be 

justified. If borrowers are unaware of these conditions, personal liability applies, and alternative 

models should be considered. Of course, alternatives are also justified for lenders who pursue 

judgments. 

Expanding on this argument, some have claimed that deficiency judgments are generally 

not an issue because related lawsuits are "rare."13 However, little empirical evidence exists to 

confirm the "rarity" of pursuit and how it should be interpreted remains unclear. Lenders should 

not be expected to pursue claims when the deficiency is small or the borrower has few resources 

to honor the liability. 14 In such cases, pursuit will be infrequent if borrowers choose to default 

only as a last resort, after all wealth is exhausted. That is, infrequent pursuit may be due to the 

insolvency of the defaulting borrower, not to the lack of lender interest or sophistication. Borrowers 

with significant wealth may continue to expect full pursuit of their deficiencies even as they 

observe infrequent pursuit of the deficiencies of others. 

Another approach is to treat deficiency judgments and other legal risks as transaction 

costs.15 These costs reduce the value of the option exercise but are otherwise consistent with the 

interpretation of default as a put. Unfortunately, this view is difficult to reconcile with the nature 

8 
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of related risks. As shown in Figure 1, the cost of a deficiency judgment equals or offsets the 

value of an option exercise: that is, judgment costs rise with option value. Moreover, the 

likelihood of a judgment depends on state law, so expected costs are analogous to dummy 

variables that either apply or do not apply, depending on the requirements of each jurisdiction. 

Since only a handful of states promote pervasive antideficiency environments, the argument has 

limited application. 

In sum, treating mortgage default as a put option can be justified in the several states 

where antideficiency restrictions are pervasive and in situations involving lenders or servicers 

who do not pursue deficiencies as a matter of policy. Conversely, it cannot be justified in many 

other legal and servicer environments. Whether one setting or the other constitutes the bulk of the 

mortgage market is an empirical issue. The point here is that there are compelling legal grounds 

for developing alternatives to put option models in substantial parts of the mortgage market. 

III. The Model 

Consider a three-period pure exchange model with no taxes. Individuals are endowed 

with time O income, part of which is invested in equity of a unit of perpetual real estate financed 

by a fixed-rate mortgage underwritten at current income (y0 ) and prices. It is assumed that 

implicit rents earned from real estate equity are fully consumed in the period received, and that 

periodic consumption ( CJ is recorded net of these earnings. 16 Initial income, real estate prices, 

and interest rates are known, but may differ from future realized values (y ;, p ;, and i J· 

Expectations are determined by a rational process whereby Y,+1 = y;,P,+1 = Pi' and i,+1 = i/. 

9 
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Unsecured borrowing (b, > 0) and lending (b, < 0) are residuals that smooth intertemporal 

consumption. 

Borrowers have three broadly defined options for revising mortgage choice after the 

initial period. First, a refinance option (Ri ) grants borrowers the periodic right to recontract the 

mortgage at lower rates in the event rates fall. To add a practical element, it is assumed that 

exercise of the refinance option requires that the underwriting variables, income, and real estate 

prices at least equal their initial amounts. Under these conditions, the option may be written as 

R/(moCio-i/) I y/q0,p/'?p0) = { max (0, m0(io-i/)) 

0 

if y/~Yo and p/'?po 

if either y/<y0 orp/<p0}, 

where m0(i0-it') is the periodic interest savings due to option exercise. Second, borrowers can also 

move to a new residence (MJ that has no income or real estate price constraints but requires 

transactions costs (MJ). 17 The move option may be written as 

Third, borrowers can default(DJ. Since default entails movement to another residence along 

with credit impairment, default transaction costs (DT) must be greater than the costs of a simple 

move, MI'. 18 The option may be written as 

where DT>MI'. Since all options have the same interest rate sensitivity, borrowers exercise only 

the most valuable option at any point in time, that is, max[R/, M/, D/]. 

Given that rational expectations project initial income and prices to all future periods, the 

refinance, move, and default options have no value, and individual choice is described by 
. 

max U(c0, Ci, c2) 

(in Co, Ci, C2) 

where (2) and (3) are cash-flow and terminal conditions, respectively. i

9 

Textbook treatments of the individual's choice focus on first- and second-order 

(1) 

(2) 

(3) 

(4) 

conditions required for a solution, such as "the optimal marginal rate of substitution in 

consumption is determined by the market rate i." However, our interests are satisfied by 

assuming that the traditional requirements for a solution are met for all reasonable parameter 

values, which implies, through (4), that the borrower is solvent throughout the term of the model. 

The genesis of this analysis is the point where actual income and prices diverge from 

expectations, which is ex post to the individual's initial choice. The role of default may be traced 

through a revised choice that responds to adverse changes in the sources of uncertainty, Yi',p 1', 

and ii' during period 1. Changes in period 2 are omitted for notional ease. Since the individual 

must honor debt obligations contracted in period 0, the revised problem may be viewed as a twoperiod choice with debt constraints imposed by prior optimizations: 

max U'( Ci', c2') 

(in ci', c/) 

ci', c/ > 0. 

11 

(2') 

(3') 

(4') 
. 

Interior solutions (ci', c2' > 0) are assumed to imply solvency, whereas comer solutions (ci', c/ 

0) imply insolvency or the exhaustion of wealth. 

Equations (2') to ( 4') recognize two distinct motivations for mortgage default. The first is 

the option-theoretic notion that default is an unusual type of refinance option facilitating an 

increase in wealth through a reduction in the mortgage coupon rate. This "strategic" default 

option is exercised solely on the basis of interest rates and the value of the option with respect to 

the value of other options capable of achieving similar savings. Hence the exercise is 

independent of income, other borrowings (savings), default on other obligations, and insolvency. 

Indeed, the increase in wealth arising from exercise of the option implies a reduction in the risk 

of insolvency. Since exercise of the strategic default option presumes borrower solvency, lenders 

are expected to pursue all legal remedies needed to collect the mortgage debt mo(l +i0). The 

model therefore applies wherever deficiency judgments can be and are commonly pursued and 

wherever borrowers assume personal liability on the basis of asymmetric legal information. 

The second motivation for default is insolvency. If any form of wealth declines 

unexpectedly, consumption is financed by savings, borrowings, or other forms of wealth 

substitution. Wealth is exhausted when consumption is no longer possible in any period in which 

extant obligations are being honored. The exhaustion of wealth is presumed to be synonymous 

with insolvency, mortgage default, and default on all other borrower obligations. In line with the 

consumer-theoretic principle that alternative forms of wealth are substitutes (the "independence" 

axiom), mortgage default is one aspect of a broad decline in consumer financial health. Hence the 

model is also consistent with the legal ability of mortgage creditors to place claims on other 

12 
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forms of borrower wealth and the ability of nonmortgage creditors to place claims on home 

equity. 

A natural incongruity exists between the strategic and insolvency motivations for default. 

Strategic default increases borrower wealth, which reduces the likelihood of default due to 

insolvency. Strategic default is independent of income and other wealth-related variables as well 

as default on other obligations, whereas insolvency default is directly tied to all wealth-related 

variables and occurs in concert with default on other obligations. The failure of option-based 

models to recognize insolvency as a motivation for mortgage default represents a limitation that 

is inconsistent with standard elements of consumer theory. 

IV. Fundamental Determinants of Default 

The fundamental determinants of default are variables capable of independently 

motivating default. As such, they may be identified by examining independent changes to the 

primary sources ofrisk,yi',Pi', and ii'- For example, holding rates constant (i 1'= i0), the 

following analysis is simplified by recognizing that default will never occur if period 1 income 

and price expectations are either realized or exceeded (y1'2::y0 and p{qy0 ) owing to the 

satisfaction of (4). 

The role of falling income in cash-flow condition (2') provides a natural starting point for 

the analysis because the failure to meet contractual debt obligations is what initiates foreclosure. 

In this regard, it is heuristic to define a "trigger" event as an unanticipated shortfall in income 

such that income is not sufficient to meet periodic debt obligations: that is, y 1 ' - moi - boi < 0 in 

(2').20 Trigger events imply that solvency can be maintained only by borrowing against 

13 
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anticipated future income or wealth, and that default occurs if borrowings are insufficient to meet 

contractual debt obligations. Trigger events may also be viewed as negative shocks to income 

that are strong enough to force the use of borrowings or savings to prevent default. 

The role of trigger events may be illustrated by examining a specific event. Holding 

other variables constant (p1'= Po and ii'= i0), letyi' O+ for the resource constraints (2') to (4'): 

lim ci' = - moi0 - boio + bi' Yi' O+ 

lim c/ 

Yi' O+ 

Solvency in period I requires borrowings against period 2 wealth to at least equal m0i0+ b0i

0, so 

default obtains if 

(5) 

Default occurs if borrowings from previous periods exceed homeowner equity. Positive 

borrowings (bo>O) imply that equity is positive at the point of indifference, whereas negative 

borrowings (b0<0) imply default when negative equity falls below savings. Positive equity has no 

consumption value if it is insufficient to cover borrowings, and negative equity does not motivate 

default as long as savings are sufficient to support the mortgage liability. Only in the special case 

ofno borrowings and no income (b0= yi'= 0) does negative equity become the sole requirement 

for default. A priori, negative equity is neither a necessary nor a sufficient condition for default, 

and default may occur when equity is positive, even in the absence of sale-related transactions 

costs. 

14 
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The importance of trigger events transcends their use as a heuristic device. Since equation 

(5) obtains for constant real estate prices and interest rates, income-related shocks constitute an 

independent class of default-related motivations. Owing to the simplicity of the framework, a 

wide variety of events can be included, such as expense-related shocks (unforeseen medical, 

legal, or other expenses), along with loss of employment or other direct shocks to income. 

Trigger events thus represent a distinct, broad class of default motivations. 

The fact that income shocks are significant by no means suggests that real estate equity 

plays no role. Holding other variables constant (y1'= Yo and i1'= i0 ), a price shock of 0+ 

implies 

lim c1' = Yo - m0i0 - boi0 + b1' 

Pi' O+ 

lim ci' = Yo - mo(l +i0) - (b0+ bi')(l +i0). 

Pi' O+ 

Default occurs if period 1 residual savings (bi'<0), invested at the rate i0• are insufficient to meet 

period 2 obligations: 

(6) 

Default is chosen when income is insufficient to honor contracted debt obligations, including 

negative equity implied by the mortgage liability, mo(l +i0)2. Negative borrowings (b0<0) reduce 

the income threshold needed to support the mortgage liability without changing the nature of the 

default decision. These results confirm that declining house prices act as a motivation for default 

and that negative equity is neither a necessary nor a sufficient condition for default. 

15 
. 

The independent role of interest rates is especially interesting as it raises the possibility of 

strategic default through the option variable max[Rt', Mi', D1']. Holding other variables constant 

(y1 '= Yo and p 1 '= Po ), declining rates increase borrower wealth as the refinance, move, and 

strategic default options come in-the-money. However, since borrowers will always choose the 

option with the highest value, and transaction costs impair the value of M1' and D1', the refinance 

option is always preferred. Put another way, the refinance option is favored over the move and 

strategic default options because it offers a lower-cost means of gaining the same value from 

declining rates. This result obtains for any level of move or default transaction costs greater than 

zero, so the level of transactions costs are of secondary importance. In any event, exercise of the 

refinance option increases wealth with respect to the initial choice problem depicted in equations 

(2) to (4), so it cannot motivate insolvency default due to satisfaction of (4). 

In the case of rising rates, the refinance, move, and strategic default options fall out-ofthe-money while having no impact on previously contracted obligations. The new choice 

constraints, 

are almost identical to those of the initial choice of (2) to ( 4 ), except for a new period 1 residual, 

b1', based on the new rate ii'. Given an interior solution to (2) to (4) for any i0 , a solution must 

also exist for any i1'>i0, implying solvency for all rate increases. Rising rates may change the 

optimal level of nonmortgage borrowing (saving) but cannot motivate insolvency if sufficient 

wealth exists prior to the rate increase to meet all obligations. 

16 
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V. Interactive Effects 

The coincident variation of combinations of y1', p 1 ', and i 1' may be classified into two 

groups: one containing only the fundamental variables (y1' and p 1') and the other either of the 

fundamental variables and interest rates (y1' or pi' combined with i1'). 

As might be expected, a decline in the two fundamental variables raises the likelihood of 

default. Holding rates constant (it'= i0 ) 

lim ct' = - moi0 - b0i0 + b1', 

(y/,pi') ➔ (O+, 0+) 

Inn c2' = - m0(l +i0) - (b0+ bi')(l +i0), 

(y/,pi') ➔ (O+, 0+) 

and the decision to default simplifies to the requirement that b0 > - m0• That is, default can only 

be averted if the borrower saves more in period O than the mortgage liability. Presumably, this 

level of savings is rare, so it seems reasonable to expect a dramatic coincident decline in income 

and house prices to virtually guarantee default. However, exceptions are possible in the event 

that savings are sufficient to maintain solvency. 

A decline in income and interest rates introduces the possibility of strategic default. 

Holding prices constant (p1'= Po), 

lim ct' = - m0i0 - b0i0 + b1' + M1' 

(y/, i1') ➔ (O+, O+) 

lim c2' = Po - mo(l+i0) - (b0+ bi')(l+i0) + M1'. 

(yt', ii') ➔ (O+, O+) 

The shock to income coupled with limits on the refinancing option cause the move option to 

become the preferred alternative for gaining value from lower rates. Exercise of the strategic 

17 
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default option is forgone in favor of the less costly move option. However, insolvency remains a 

possibility, as shown by combining the above limits: 

(7) 

which is identical to (5) except for the additional value of the move option, Mi'(2+i0). The 

general conclusions surrounding (5) continue to hold, although the level of unsecured borrowings 

required for insolvency must be larger by the value of the move option. Whereas declining 

wealth caused by declining income increases the likelihood of insolvency, increased wealth due 

to declining rates has the opposite effect. The strategic default option is never exercised because 

it is the highest cost alternative for gaining wealth from declining rates. 

Combining a decline in interest rates and house prices is especially interesting as it is 

cited in option-based discussions. Holding income constant (yi'= y0) 

lim Ci' = Yo - moi0 - boi0 + bi' + Mi', 

(pi', ii') ➔ (O+, O+) 

lim c2' = Yo - mo(l+i0) - (b0+ bi')(l +i0) + Mi'-

(pi', ii') ➔ (O+, 0+) 

Exercise of the strategic default option is again forgone in favor of the less costly move option, 

the exercise of which increases wealth. Default due to insolvency occurs when 

(8) 

which extends (6) to include the additional value of the move option, M1'(2+i0). Declining wealth 

associated with declining house prices is at least partly mitigated by increasing wealth caused by 

declining rates. The income and borrowing thresholds required for insolvency are necessarily 

reduced by the addition to wealth arising from lower rates and exercise of the move option. The 

strategic default option is never exercised because lower-cost alternatives are available. 

18 
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The roles of interest rates and unsecured borrowings should also be mentioned. Since 

these variables are found throughout the various conditions for default, they clearly affect default 

by establishing constraints that interface with shocks to Yi' and Pi' to motivate insolvency. The 

variables may also act as signals in the absence of complete information on changes inyt' and 

Pt'. In the case of declining interest rates, a default observed when the refinance option is in-themoney (i/<i0) may be the result of unobserved negative shocks to either Yt' or Pt'· For similar 

reasons, default might also be associated with an increase in other borrowings. However, if the 

the fundamental determinants of default are fully identified, both variables should cease to 

provide empirical significance. 

To summarize, mortgage default is due primarily to insolvency in legal and economic 

settings for which the choice-theoretic model applies. Income and real estate prices are 

fundamental determinants of default because shocks to either variable may erode homeowner 

wealth to the point of insolvency. Declining interest rates cannot independently motivate 

insolvency because they increase wealth through the refinance option. Although homeowners 

posses a strategic default option capable of capturing a portion of the value of declining rates, 

this option is never exercised as long as refinance and move options provide less expensive 

alternatives for generating the same value. Therefore, to the extent that a two-variable paradigm 

explains mortgage default, the relevant variables are income and house prices, not interest rates 

and house prices. 

19 
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VI. Empirical Issues 

As explained earlier, alternatives to option-based models appear to be warranted in most 

jurisdictions. The empirical implications of the choice-theoretic model are of particular interest 

here, as they pertain to observations and regularities that are inconsistent with, or otherwise 

difficult to explain by, option-based models. These include the following: 21 

1. Many borrowers who default cite the reason as loss of income, divorce, and other 

tragic events bearing no apparent relation to changes in the value of home equity. 

2. Large percentages of delinquent borrowers cure their delinquencies prior to 

foreclosure. 22 

3. Bifurcated default patterns have not been observed. Low levels of default have been 

reported throughout the United States in all economic environments, whereas universal 

default has not been observed in areas characterized by extended periods of declining 

house prices. 23 

4. Empirical tests fail to uncover a consistent relationship between interest rates and 

default. 

5. Empirical tests often uncover significant relationships between default and 

unemployment, income, or other variables having no clear role in option-based models. 

6. Mortgage default is closely associated with default on other borrower obligations. 

7. An active market exists for mortgages with original LTV s of up to 125 percent. 

The choice-theoretic model provides a framework for understanding these characteristics 

of mortgage default. To begin with, trigger events help to explain default arising from loss of 

20 
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employment, divorce, and other tragic events that independently affect income. The central role 

ascribed to trigger events is highly consistent with borrower's reports that income-related shocks 

are common reasons for default. 24 

Building on Friedman (1957), trigger events may vary based on two types of incomerelated shocks. The first is a shock to current income that induces a similar shock to anticipated 

future income ("permanent" income), as occurs when an occupation becomes obsolete and 

causes long-term loss of employment. The "rational" adaptation of income assumed in (2') to 

( 4') reflects these changes. Permanent shocks greatly increase the likelihood of default because 

they imply cash-flow problems in future as well as current periods. The second type of shock is a 

temporary event that does not affect permanent income, such as a temporary layoff. These shocks 

are less problematic because they constrain only current cash flows, and have little impact on 

future income or the ability to borrow against that income. 25 

The "permanence" of income shocks leads large percentages of delinquent borrowers to 

cure their delinquencies before default. The fact that temporary income shocks are relatively 

common accounts for the high 30- and 60-day single-family delinquencies.26 Foreclosure may 

occur only for successions of temporary shocks and for permanent shocks. In option models, 

however, the fundamental determinants of default are changes in house prices and interest rates, 

which implies that a primary motivation of cures is directional changes to these variables. 27 

Although option models may be extended to include liquidity constraints or other factors to 

explain observed delinquency patterns, they focus primarily on shocks to interest rates and house 

prices and thus provide little insight into these pattems.28 

21 
. 

Income-related variables also account for the lack of bifurcated default patterns. Since 

borrower-specific income shocks are possible in any region at any time, defaults should be 

minimal at every meaningful level of aggregation (states, cities, etc.) and for any period or rate of 

house price appreciation. Similarly, significant numbers of local populations typically retain their 

employment and income during periods of declining house prices, so universal default should 

never be observed, even at low levels of aggregation and at LTVs implying negative equity. 

Put option models unanimously posit that interest rates are as closely related to default as 

house prices. However, empirical evidence has failed to consistently support this hypothesis.29 As 

discussed earlier, the choice-theoretic model suggests that interest rates do not motivate default, 

although they may be found to correlate with default absent complete information on shocks to 

income and house prices. 

Although empirical work has failed to verify a clear role for interest rates, it commonly 

finds other significant variables to be inconsistent with option-based models. For example, recent 

tests include dummy variables for specific states, unemployment, income, and income growth. 30 

Less technical analyses, as well as rating agency models, tend to stress a broader range of 

variables, including property type, mortgage type and purpose.31 Variables along these lines are 

generally inconsistent with put option models, but consistent with the choice-theoretic notion 

that borrower income, savings, and borrowings combine with real estate equity to explain 

default. 

That other aspects of borrower financial health may play a role in default is suggested by 

the close association between mortgage default and default on other obligations. As already 

mentioned, option-based models treat mortgage choice as separable from other aspects of 

22 
. 

borrower health; by contrast the choice model implies that delinquencies for all types of debt 

should be closely linked. The choice model is most consistent with increasing use of borrower 

credit scores in automated underwriting and high-risk lending activities, such as those discussed 

by Mahoney and Zorn (1996) or Lieberman (1996). 

Mortgages with LTVs as high as 125 percent are also anomalous to put option models. 

Although these mortgages are typically subordinated interests, option-based hypotheses extend to 

them and imply that they should virtually always default. However, Lieberman (1996) finds a 

number of issuers populating this market in the belief that "borrower capacity and credit quality" 

mitigate the risk of "negative borrower equity." Between 1990 and 1995 average annual chargeoffs on related securitizations were a modest 3-6 percent. While high-LTV mortgages remain a 

relatively new product and credit quality has not yet been fully tested, they serve as a market 

statement that real estate equity is not the only determinant of mortgage default. 

A final comment relates to previous tests of income-related variables. While these 

variables are found significant in many tests, they nevertheless often fail to capture the full 

impact of income and income-related shocks. For example, one variable, income at origination, 

fails to reflect changes to income following origination in the same manner that LTV at 

origination fails to reflect changes in house prices. This is especially a problem for income 

because large shocks may occur at any time following origination.32 Another measure, average 

income at county, state, or other levels, may remain unchanged even as significant numbers of 

borrowers experience income shocks. Alternatives reflecting recent changes to individual income 

are much preferred to either income at origination or average income at almost any level of 

aggregation. 

23 
. 

II. Conclusion 

Although mortgage default is now widely treated as a put option, there is little basis for 

asserting the rights associated with a put in many jurisdictions. In these environments the cost or 

risk to borrowers arising from lender pursuit of remedies erases the primary economic benefit of 

treating mortgage default as a put option while justifying the development of alternative models 

of mortgage default. 

The choice-theoretic model proposed here is generally consistent with mortgage laws in 

many jurisdictions as well as the notion that home equity is substitutable with other forms of 

income and wealth. The model attributes mortgage default to borrower insolvency. Variables 

related to income and real estate price variables are identified as the fundamental determinants of 

default because they precipitate insolvency through the erosion of wealth. The substitutability of 

income, borrowings, and other forms of wealth implies that negative equity is neither a necessary 

nor a sufficient condition for default, even in the absence of sale-related transactions costs. 

Declining interest rates cannot independently motivate default due to insolvency because they act 

to increase wealth through the refinance option. Although homeowners posses a strategic default 

option capable of capturing a portion of the value of declining rates, they will not exercise this 

option as long as refinance and move options provide less expensive alternatives for generating 

the same value. Therefore, to the extent that a two-variable paradigm explains mortgage default 

whereever put option models are not applicable, the fundamental variables are income and house 

prices, not interest rates and house prices. 

The model developed here appears to explain many empirical characteristics of mortgage 

default that are inconsistent with, or otherwise difficult to explain by, option-based models. The 

24 
. 

model echoes reports by defaulted borrowers that blame their default on loss of income, divorce, 

and other tragic events having no apparent relation to homeowner equity. The model also 

explains other findings, ranging from the observation that delinquent borrowers commonly cure 

their delinquencies before foreclosure to a market of mortgages with LTV s of up to 125 percent. 

The model therefore promises considerable empirical application while offering a framework for 

understanding default in environments for which put option models do not apply. 

25 
. 

References 

Abrahams, Steven W. 1997. "The New View in Mortgage Prepayments: Insight from Analysis at 

the Loan-by-Loan Level." Journal of Fixed Income 7(1): 8-21. 

Asay, M. R. 1978. "Rational Mortgage Pricing." Ph.D. dissertation, University of Southern 

California, Los Angeles, and Research Paper in Banking and Financial Economics, no. 30 (Board 

of Governors of the Federal Reserve System, 1979). 

Ambrose, Brent W., and Charles A. Capone. 1996a. "Resolution of Single-Family Borrower 

Default: Modeling the Conditional Probability of Foreclosure." Paper presented at the Mid-Year 

AREUEA Meetings, Washington, D.C. 

Ambrose, Brent W., and Charles A. Capone. 1996b. "Cost-Benefit Analysis of Single-Family 

Foreclosure Alternatives." Journal of Real Estate Finance and Economics 13(2): 105-20. 

Ambrose, Brent W., Richard J. Buttimer, Jr., and Charles A. Capone Jr. 1997. "Pricing Mortgage 

Default and Foreclosure Delay." Journal of Money, Credit, and Banking (forthcoming). 

Archer, Wayne R., David C. Ling, and Gary A. McGill. 1996. "The Effect oflncome and 

Collateral Constraints on Residential Mortgage Terminations." Regional Science and Urban 

Economics 26(3): 235-61. 

Campbell, T. S., and J. K. Dietrich. 1983. "The Determinants of Default on Insured Conventional 

Residential Mortgages." Journal of Finance, 38(5): 1569-81. 

Capone, Charles A. Jr. 1994. "The Theory of Non-Optimal Mortgage Default." Paper presented 

at the Mid-Year AREUEA Meetings, Washington, D.C. 

Case, Karl E., and Robert J. Shiller. 1996. "Mortgage Default Risk and Real Estate Prices: The 

Use oflndex-Based Futures and Options in Real Estate." Journal of Housing Research 7(2): 

243-58. 

Crandall, Thomas D., Richard B. Hagedorn, and Frank W. Smith. 1991. The Law of Debtors and 

Creditors, (Boston, Mass.: Warren, Gorham, & Lamont). 

Cunningham, Donald F., and Patric H. Hendershott. 1984. "Pricing FHA Mortgage Default 

Insurance." Housing Finance Review 3(4): 373-92. 

Deng, Yongheng. 1997. "Mortgage Termination: An Empirical Haz.ard Model with a Stochastic 

Term Structure." Journal of Real Estate Finance and Economics 14(3): 309-31. 

26 
. 

Deng, Yongheng, John C. Quigley, and Robert Van Order. 1995. "Mortgage Default and Low 

Down Payment Loans: The Costs of Public Subsidy." National Bureau of Economic Research, 

Working Paper no. 5184. 

Dunaway, Baxter. 1995. The Law of Distressed Real Estate: Foreclosure, Workouts, Procedures. 

Deerfield, Ill.: Clark Boardman Callaghan. 

Elmer, Peter J., and Anton E. Haidorfer. 1997. "Prepayments of Multi-family Mortgage-Backed 

Securities." Journal of Fixed Income 6(4): 50-63. 

Fama, Eugene F., and Merton H. Miller. 1972. The Theory of Finance. Hinsdale, Ill.: Dryden 

Press. 

Fitch Investors Service, Inc. 1993. "Fitch Mortgage Default Model." Fitch Research Structured 

Finance Special Report, June 28. 

Friedman, Milton. 1957. A Theory of the Consumption Function. Princeton, N. J.: Princeton 

University Press. 

Foster, Chester, and Robert Van Order. 1984. "An Option-Based Model of Mortgage Default." 

Housing Finance Review 3(4): 351-72. 

Gardner, Mona J., and Dixie L. Mills. 1989. "Evaluating the Likelihood of Default on 

Delinquent Loans." Financial Management 18(4): 55-63. 

Hendershott, Patric H., and Robert Van Order. 1987. "Pricing Mortgages: An interpretation of 

the Models and Results." Journal of Financial Services Research 1(1): 19-55. 

Jones, Andrew B., Henry W. Hayssen, and Jennifer E. Schneider. 1995. "Rating of Residential 

Mortgage-Backed Securities." Journal of Fixed Income 4(4): 12-36. 

Jones, Lawrence D. 1993. "Deficiency Judgments and the Exercise of the Default Option in 

Home Mortgage Loans." Journal of Law and Economics 36(1): 115-38. 

Kau, James B., Donald C. Keenan, Walter J. Muller, and James F. Epperson. 1992. "A 

Generalized Valuation Model for Fixed-Rate Residential Mortgages." Journal of Money, Credit, 

and Banking, 24(3): 279-99. 

Kau, James B., Donald C. Keenan, Walter J. Muller, and James F. Epperson. 1993. "Option 

Theory and Floating-Rate Securities with a Comparison of Adjustable- and Fixed-Rate 

Mortgages." Journal of Business 66(4): 595-618. 

27 
. 

Kau, James B. and Donald C. Keenan. 1995. "An Overview of the Option-Theoretic Pricing of 

Mortgages." Journal of Housing Research 6(2): 217-44. 

Kau, James B., Donald C. Keenan, Walter J. Muller, and James F. Epperson. 1995. "The 

Valuation at Origination of Fixed-Rate Mortgages with Default and Prepayment." Journal of 

Real Estate Finance and Economics 11(1): 5-36. 

Lekkas, Vassilis, John M. Quigley, and Robert Van Order. 1993. "Loan Loss Severity and 

Optimal Mortgage Default." Journal of the American Real Estate and Urban Economics 

Association, 21(4): 353-71. 

Lieberman, Jonathan. 1996. "Low and No Equity Second Mortgage Loans: Credit Card Debt 

Moves to Mortgage Land." Moody's Investor Service Structured Finance Special Report, 

November 15. 

Mahoney, Peter E., and Peter M. Zorn. 1996. "The Promise of Automated Underwriting." 

Secondary Mortgage Markets 13(3): 18-23. 

Merton, Robert C. 1973. "A Rational Theory of Option Pricing." Bell Journal of Economics and 

Management Science 4(1): 141-83. 

Monsen, Gordon. 1996. "A Poor Performance." Mortgage Banking, 14-22. 

Moody's Investor Service. 1990. "Moody's Approach to Rating Residential Mortgage PassThroughs." Special Report of Moody's Structured Finance Research and Commentary, April. 

Nelson, Grant S., and Dale A. Whitman. 1993. Real Estate Finance Law. (3rd ed. St. Paul, 

Minn. West. 

Phillips, Richard A., Eric Rosenblatt, and James H. V anderhoff.1996. "The Probability of Fixed 

and Adjustable-Rate Mortgage Termination." Journal of Real Estate Finance and Economics 

13(2): 95-104. 

Quigley, John M., and Robert Van Order. 1995. "Explicit Tests of Contingent Claims Models of 

Mortgage Default." Journal of Real Estate Finance and Economics 1(2): 99-117. 

Riddiough, Timothy, J. 1991. "Equilibrium Mortgage Default Pricing with Non-Optimal 

Borrower Behavior." Ph.D dissertation, University of Wisconsin. 

Schwartz, Eduardo S., and Walter N. Torous. 1992. "Prepayment, Default, and the Valuation of 

Mortgage Pass-Through Securities." Journal of Business 65(2): 221-39. 

Vandell, Kerry D. 1995. "How Ruthless is Mortgage Default? A Review and Synthesis of the 

Evidence." Journal of Housing Research 6(2): 245-64. 

28 
. 

U.S. Department of Housing and Urban Development. 1996. "Providing Alternatives to 

Mortgage Forclosure: A Report to Congress." March. Washington, D.C.: U.S. Government 

Printing Office. 

von Furstenburg, George M., and R. Jeffrey Green. 1974. "Estimation of Delinquency Risk for 

Home Mortgage Portfolios." AREAUA Journal 2(1): 5-19. 

Wilson, Donald G. 1995. "Residential Loss Severity in California: 1992-1995." Journal of Fixed 

Income 5(3): 35-48. 

29 
. 

Notes 

1 The proposition was first suggested by Asay (1978), then extended and popularized by Foster 

and Van Order (1984). A recent sample of literature can be found in Schwartz and Torous (1992), 

Kau et al. (1992, 1993, and 1995), Kau and Keenan (1995), Vandell (1995), and Deng (1997). 

2 As emphasized by Lekkas, Quigley and Van Order (1993) and Quigley and Van Order (1995), 

"the virtue of the contingent claims model is its simplicity." Only variables relating to option 

exercise should have an impact on the default decision, and there are no costs to default other 

than losing the house. Given this perspective, it is not surprising that many option-based 

discussions cited in note 1 include no mention of borrower insolvency. Vandell (1995) provides 

an exception with a call to "understand better the role that solvency plays in mortgage default." 

3 See Monsen (1996) or Mahoney and Zorn (1996). 

4 Early tests are performed by von Furstenburg and Green (1984) and Campbell and Deitrich 

(1983). Recent work includes that of Wilson (1995); Jones, Hayssen, and Schneider (1995); 

Deng, Quigley, and Van Order (1995); Monsen (1996); Phillips, Rosenblatt, and Vanderhoff 

(1996); Case and Shiller (1996), and Deng (1997). 

5 Jones et al. (1995) describe a model used by Duff and Phelps in which risk is based on negative 

equity, mortgage type (fixed-versus-adjustable-rate), borrower credit quality, occupancy, and 

other variables. Similar models can be found in Fitch (1993) and Moody's (1990). Mahoney and 

Zorn ( 1996) describe automated underwriting technology that takes a similar approach. 
. 

6 More extensive legal analysis may be found in Dunaway (1995), chaps. 12-14, and Nelson 

and Whitman (1993), chaps. 7-8. U.S. Department of Housing and Urban Development 

(1996), chap. 6, provides an overview of the subject. 

7 For legal discussions of foreclosure and deficiency judgments, see Nelson and Whitman (1993), 

§§ 8.1-8.3. Apart from deficiency judgments, lenders may also obtain a judgment on the personal 

obligation (note) and enforce it by levy upon any property of the borrower. A third alternative is 

to protect the contract in the mortgage agreement. For example, the Veterans Administration 

contracts an indemnity certifying that the borrower is legally obligated to make the mortgage 

payments called for by the mortgage contract. 

8 Jurisdictional variations detailed by Dunaway (1995), appx. 14A, show California, Arizona, and 

Alaska as three states with pervasive antideficiency environments. At least two additional states 

(Montana and Oregon) broadly prohibit deficiency judgments for purchase money mortgages. 

South Dakota also restricts the area of purchase money mortgages, but only when the mortgagee is 

also the vendor; i.e., the seller is doing the financing. 

9 For example, FNMA's servicing requirements, dated August 31, 1994, state that "the servicer 

should diligently seek out, and recommend to Fannie Mae, appropriate cases in which the pursuit of 

a deficiency judgment should be considered." FHLMC requirements, as of May 1, 1996, require 

that servicers "identify and recommend appropriate cases where the pursuit of deficiency judgments 
. 

is in FHLMC's best interest." More than 20 private specialists participated in the Resolution Trust 

Corporation's (later the Federal Deposit Insurance Corporation's) 1994 limited partnership program 

to resolve approximately $7 billion (face value) of judgments, deficiencies, and charge-offs. 

Information on participants in this program is available through the FDIC's Public Information 

Center. 

10 See Crandall, Hagedorn, and Smith (1991), § 6.05[2]. Further docketing is required to acquire 

liens in other counties of the state in which the judgment is rendered. 

11 Residential real estate also has drawbacks as a mechanism for satisfying claims. Litigation and 

other legal action is costly and time consuming. Although it is possible for any party with an 

interest in the real estate to redeem, it is often unlikely that any would to do so as long as first- or 

second-mortgage interests precede their claim. If the borrower remains current on secured 

obligations, other lien holders may be forced to wait until sale before collecting on the claim. 

12 This application treats the entire interest payment mi as the option premium, which limits the 

discussion to option-related issues. Though it is widely accepted that the mortgage rate contains 

real and inflation components alongside a premium for default risk, these elements need not be 

considered for purposes of this discussion. 

13 See Kau and Keenan (1995) or Case and Shiller (1996). 
. 

14 The FNMA Servicing Guide cites a variety of factors to consider, such as the amount of the 

deficiency, the cost of pursuing the judgment in relation to the amount of the deficiency, and the 

probability of a favorable judgment. 

15 See Cunningham and Hendershott (1984) or Hendershott and Van Order (1987). Ambrose, 

Buttimer, and Capone (1997) specify an option-based model that includes the cost of deficiency 

judgments as a probabilistic event. 

16 This assumption arises from the notion that single-family real estate is a required consumption 

good that simultaneously serves as an investment. Implicit rents received by the individual's 

investment account are matched by implicit payments from his or her consumption account, with 

no cash flow exchange. Individuals might otherwise rent their residential investments to other 

parties, while using rents received to support rents paid for real estate services from other 

investors. 

17 The right to move is widely acknowledged and contractually supported by the prepayment and 

"due on sale" clauses of the standard FHLMC-FNMA note and mortgage. The move option 

represents an alternative to default that does not involve either a breach of contract or personal 

liability for damages. Move options are generally not acknowledged in option-based models of 

mortgage default, although they can be found in many prepayment discussions. See, for 

example, Archer, Ling, and McGill (1996); Abrahams (1997); and Elmer and Haidorfer (1997). 
. 

18 Capone (1994) develops a model of foreclosure choice that includes the option to move. This 

model finds property sale preferred to foreclosure for reasonable parameter values. 

19 The three-period model is easily extended to include an arbitrary number of period 1 cash 

flows or period 2 terminal conditions. See, for example, Fama and Miller ( 1971 ), chap. 1. 

20 Although the term "trigger" event has been used often, it is typically not formally defined or 

linked to specific income or wealth-related variables. For example, Riddiough (1991) and Deng 

(1997) integrate trigger events into option-based models as stochastic shocks, but fail to specify 

the economic character of the events or their link to wealth-related variables. 

Previous references to trigger events appear to view them as synonomous with default but 

independent of interest rates and house prices. However, the choice-theoretic framework raises 

questions regarding this approach. Holding house prices and interest rates constant, will a given 

trigger event, such as unemployment, cause default for all borrowers? The choice-theoretic 

model suggests that unemployment will impact borrowers differently based on differences in 

other borrowings (savings). If trigger events are defined as always causing default, then their 

magnitude must differ by borrower to account for varying wealth positions. 

This paper views trigger events as a broad class of income- or expense-related events that 

cause periodic liquidity problems. This approach makes sense in a two-period model because 

there is little distinction between short- and long-term results. However, the approach has less 

appeal in extended models with many periods, where a single-period shock has less impact on 

borrower choice. 
. 

21 Additional concerns are raised by Lekkas, Quigley and Van Order (1993) and Quigley and Van 

Order (1995) findings that loss severity is closely related to the initial loan-to-value (LTV} ratio. 

22 See delinquency statistics in "National Delinquency Survey," published by the Mortgage 

Bankers Association of America (MBA). These data show 30-day delinquencies about 4 to 5 

times higher than 60-day delinquencies, 60- and 90-day delinquencies about equal, and 90-day 

delinquencies about 2 times higher than foreclosures. This pattern of declining rates is observed 

throughout the history of the MBA data. 

23 Although little empirical work has examined this issue, a variety of data strongly suggest 

minimal, bifurcation. MBA data over the past 15 years show that state foreclosure rates almost 

never exceed 1 percent (usually below 0.5 percent), with material delinquencies and foreclosures 

in all states every quarter. Defaults and foreclosures are continuously observed even in states 

experiencing house appreciation for periods as long as a decade. See, for example, state house 

price indexes for Oregon and Washington published by the Office of Federal Housing Enterprise 

Oversight. Jones, Hayssen, and Schneider (1995) cite cumulative default rates of only 13% as 

representing the "extremely severe" economic conditions of Houston during the 1982-88 period. 

24 See Gardner and Mills (1989) or Ambrose and Capone (1996a). 
. 

25 The mechanics ofa temporary shock can be seen by replacingYJ'withy0 in (3') and addingy0 

to the right-hand side of (5). The role ascribed to temporary shocks is consistent with Capone's 

( 1994) point that delinquency may be used as a method of financing consumption. 

26 Elmer and Haidorfer (1997) note that multifamily mortgages have lower 30- and 60-day 

delinquency rates than single-family mortgages, but higher 90-day, foreclosure, and real estateowned rates. This observation, coupled with the notion that multifamily mortgages are often 

contracted on a nonrecourse basis, suggests that they may provide an appropriate setting for 

applying put option models to the analysis of mortgage default. 

27 This view provides an appealing backdrop to the Ambrose and Capone ( 1996b) theme that 

liquidity constraints are a key aspect of single-family delinquencies. Indeed, the choice-theoretic 

model provides a formal framework for understanding the motivation and nature of liquidity 

constraints. 

28 See Ambrose and Capone (1996b). 

29 See Phillips, Rosenblatt, and Vanderhoff (1996); Lekkas, Quigley, and Van Order (1993), 

Quigley and Van Order (1995); and Jones (1993). 

30 See Deng (1997); Case and Shiller (1996); and Philips, Rosenblatt, and Vanderhoff (1996). 

31 See Monsen (1996); Wilson (1995); and the references in footnote 5. 
32 The volatility of borrower income is expected to be much higher than the volatility of 

individual house prices. Borrower income might fall to zero, or rise dramatically, within a few 

months (or even days) following mortgage origination. In contrast, house prices usually change 

little in similar time periods and otherwise tend to move slowly over time.