A contingent claim analysis of preferential rate mortgages

CHAPTER ONE: 1. INTRODUCTION In a country where citizens own more real estate assets than stocks, the valuation of Singapore real estate assets and its related financing instruments becomes a critical research agenda for the country. A government study (Singapore Department of Statistics, 2003) of Singapore household wealth and liabilities as of end of 2001 reveals that 48.2 percent of the households’ assets are in property and 72 percent of the liabilities are in mortgage loans. The key concern here, as a result of this survey, is that any change in policies or economic shocks in the real estate market will have deep and wide ranging effects on the general economy since households are highly exposed to the real estate sector. A recent change of housing and financing policies (Economic Review Committee, 2002) in Singapore, as part of the economic restructuring programme, had sparked off a wave of loan wars in the mortgage lending sector. In view of the variety and complexity of mortgages available on the market, there is considerable interest in the valuation and analysis of these financing instruments. Preferential rate mortgages1 (PRMs), being the most prevalent type of mortgage in Singapore, lacks such a framework for the benefit of the mortgagor and mortgagee to facilitate comparison and pricing. In addition, as a result Preferential Rate Mortgages (PRMs) are adjustable rate mortgages (ARMs) that provide below-market interest rate over a specified promotional term of three to five years. PRMs are quite similar in structure to US market’s ARM with teaser rates. Their main difference lies in the fact the teaser rates exist only for the first year whereas the promotional rates of PRM can last up to five or six years. In addition, most PRM uses a combination of fixed and floating promotional rates whereas ARM with teaser rates uses either floating or fixed teaser rates. of the economic restructuring, the priority of charges on mortgages has been reversed which in turn boosts the incentives to develop a secondary market for mortgages. In the light of such dynamic changes, we develop a mortgage theoretic option pricing model to accommodate the pricing, comparison and analysis of PRMs. We believe that the development of such a valuation model will also contribute to the development of mortgage-backed securities in Singapore. 1.1 Background Economic Restructuring in Singapore In Dec 2001, the government had initiated an economic review committee (ERC) against the backdrop of a significantly changed regional and world environment to fundamentally review Singapore’s development strategy, and formulate strategies to upgrade, transform and revitalize the economy (Economic Review Committee, 2002). Seven SubCommittees and numerous working groups were formed to study issues such as taxation, wages, the Central Provident Fund (CPF) and land; promoting entrepreneurship and internationalization of Singapore companies; upgrading and growing the manufacturing sector; developing the services sector; growing domestic enterprises; developing our human capital; and helping Singaporeans to respond to changes and take advantage of new opportunities. The key concerns for our study, arising from the restructuring initiatives, are the changes to the real estate financing policies. These include the imposition of a CPF valuation withdrawal limit on bank mortgages, transfer of future public housing market rate loans from the public housing authority to commercial mortgage lenders, changes to the CPF charge on a private property which is mortgaged, and changes to the cash downpayment requirement on mortgages. Mortgage Loan War As part of the economic restructuring initiatives, the government had slowly devolved some non-core Housing Development Board (HDB) functions to the private sector which includes the transfer of future public housing market rate loans to commercial mortgage lenders. This means that from 1st Jan 2003, the housing board will no longer grant loans at market interest rate to buyers of new and resale HDB flats and these buyers must take up their mortgage with an approved bank or finance company. In addition, current HDB flat owners can choose to refinance their loans with these banks and finance companies. The move had opened up a previously untapped segment of the market to the private sector that is worth $3.2 billion. As anticipated, the move had resulted in an eruption of mortgage loan war in Dec 2002 which involves not only banks, but also finance companies and even insurance companies. The ferocity in the pursuit for market share in the housing loan market prompted lenders to aggressively slash their first and second year mortgage rates down to as low as 1.5%. In addition, lenders are also coming up with various novel and competitive PRM packages to beat the competition. In view of the variety and complexity of PRMs available on the market, potential borrowers are often perplexed by the choice of mortgage package. Thus, we believe that a platform for assessment and comparison of PRMs is essential not only for the benefit of mortgagees but also mortgagors. This study attempts to fulfill this need by providing a valuation framework for PRMs. Securitization Potential of Mortgages in Singapore A recent Singapore Department of Statistics survey reveals that the amount of outstanding mortgage held by households as of end of 2001, comprising of both HDB and private sector mortgages, totaled $105.79 billion (Singapore Department of Statistics, 2003). These mortgages take the form of either adjustable-rate mortgages (ARMs) or preferential rate mortgages (PRMs). The Monetary Authority of Singapore’s (MAS) recommendations in 1998 to deepen the debt markets have led to increased interest in the securitization of this mortgage pool. However the lack of institutional and regulatory framework for MBS and the complexity of the mortgage instrument have slowed down efforts to develop the mortgage-backed securities. Against the backdrop of a high liquidity and low interest rate environment, securitization efforts had been drawn into a standstill situation. One of the major impediments for securitization is that banks not assume priority charge over the mortgaged property ahead of other institutions. In the case of foreclosure, banks having the second charge may not be able to recover the full loan amount as the Central Provident Fund, a statutory board in charge of compulsory savings for a retirement fund in Singapore, had the first charge over the foreclosed proceeds. This has deterred securitization efforts as MBS investors would not want to assume such foreclosure risk in the event of default (Nang et al, 2003). A recent change in policies resulting in the reversal of the charge position had renewed interest in securitization of mortgages. As real estate securitization in Singapore is still in its infancy, the potential for the development of a mortgage secondary market is now immense. Therefore, we believe the development of a mortgage valuation framework that thoroughly analyzes the intricate features of PRM could increase the pace of securitization and contribute toward a secondary market for PRMs. 1.2 Justification of Research PRMs may soon dominate the mortgage portfolio in Singapore Mortgages in Singapore take the form of either PRMs or ARMs in which most ARMs are provided by the public housing authority. With the cessation of HDB granting market rate loans, future buyers of new and resale HDB flats who are not eligible for concessionary loans will have to take up PRMs with the private sector. In the current low interest rate environment, many current HDB loan mortgagors are also refinancing their mortgages with private financing institutions. In the light of such changes, PRMs’ share of the market will continue to expand and may soon become the dominant type of mortgage in the market. Policymakers, mortgage lenders, borrowers and potential mortgage investors would hence be interested in understanding the pricing, risks and returns of these mortgages. Yet, no robust valuation and analytical framework exist for PRMs. This provides the impetus to develop such a framework. Valuation of PRMs is necessary for the structuring of mortgage-backed securities The idea of real estate securitization in Singapore was mooted by the MAS in 1998, as part of a plan to develop the domestic capital markets. However the development of mortgage securitization is slow due to the high liquidity and low interest environment as well as the lack of regulatory and institutional framework. With the reversal of the charge position on mortgages, the incentives for lenders to securitize their mortgages to raise liquidity have consequently increased. Prepayment and default risks are key concerns in securitized mortgages and the financial community would have a strong interest in understanding such risks before the structuring of mortgage-backed securities. In this study, we foresee the need of an analytical framework which provides a comprehensive understanding of the default and prepayment risk in mortgages. Inability of current valuation models to handle the complexity of PRMs The traditional method of valuing assets is to a net present value (NPV) calculation of the asset’s cashflows. The net present value, however, is based on some implicit assumptions that are overlooked in the pricing of mortgages. The orthodox theory of valuing assets has not recognized the interplay of irreversibility, uncertainty and the choice of timing that will determine the optimal default, prepayment and continuation decisions of mortgagors. The reason is that a borrower with an opportunity to prepay is holding a “prepayment option” analogous to a financial call option-he has the right but not the obligation to buy out future mortgage payments at some future time of its choosing. When a mortgagor prepays a mortgage, he makes an irreversible decision and gives up future opportunities to terminate the mortgage. The lost opportunities are opportunity cost that must be part of the cost of prepaying the mortgage. The NPV calculations fail to capture such rights and opportunities. Similarly, mortgagors also hold a “default option” analogous to a financial put option in which the borrower has the right to sell out the possession of the house in exchange for the abandonment of mortgage payments. Thus mortgages are usually modeled as a fixed income security with two embedded options, namely prepayment option and default option. However, it is more complicated when preferential rate mortgages come into the scenario given that the mortgage has features of both fixed and variable cashflows. In this study, we further develop the theory of mortgage valuation under uncertainty, emphasizing the option-like characteristics of mortgage termination behavior. Increasing need for mortgage lenders to evaluate risk in their mortgage portfolio Since the Asian Financial Crisis, lenders are increasing aware of the vulnerability of their banking system to external economic forces. Using data from MAS, Development Bank of Singapore (DBS) market research team found that as of May 2004, property related lending accounts for at least 46 percent of the lending by banks in Singapore (Koh, 2004). Given that the real estate collateral and mortgages form a significant portion of the bank’s asset and liabilities, lenders recognize the increasing need to understand, evaluate and benchmark the risk in their mortgage portfolio. To so, as an initial starting point, a structural model is necessary not only to identify the sources of risk but also to generate the entire risk distribution. Using option-pricing ideologies, we attempt not only to reveal the sources of risk but also to produce such risk distribution in our model. We believe that such information would be of interest to lending institutions, the central bank and the mortgage investing community. 1.3 Objectives of Research 1. To create a theoretical option pricing model to price PRMs. 2. To provide a framework whereby different PRMs can be evaluated using Option Pricing theory. 3. To provide a risk-evaluation framework for PRMs. 4. To examine how different economic and mortgage contractual factors affect the mortgage value and risk distribution. 1.4 Organization of Thesis The following chapters of this thesis are organized as follows: A review of the literature related to theoretical mortgage OPMs follows in the next chapter. Chapter presents the research methodology, viz the subject of study, techniques used and the various research innovations. The simulation results of our model are then presented in Chapter 4. This thesis shall be concluded and recommendations will be made in the final chapter. CHAPTER TWO 2. LITERATURE REVIEW This section reviews the theoretical works on the pricing of mortgages as derivative assets, often termed the option-pricing approach to mortgage valuation (Kau and Keenan, 1995). The options approach recognizes the value of the right to prepay or default in a mortgage, following the seminal work on pricing options by Black and Scholes (1973) and Merton (1973). Default can be regarded as a European compound put option where the borrower has the right to turn over the possession of the house in exchange for the abandonment of payments. The option is European because such default rationally occurs when a payment is due, and compound because there is a succession of payments over the life of the mortgage. Similarly, the right to prepay can be considered an Americanstyle call option, in which the borrower has the right to buy all future obligations remaining under the mortgage at a price equal to the loan’s outstanding balance. Default and prepayment have value in that they both have exercise value and time value. The default and prepayment options both have exercise value as the borrower receives a premium payoff when they exercise the relevant option. They have time value as the borrower is able to postpone termination of the mortgage by at least one period to see if the termination will be more optimal. Note that the two options are mutually competing in nature- that is if default occurs, the value of prepayment becomes zero; if prepayment occurs, the value of prepayment becomes zero. The two options will compete, so that the 10 In addition, we wish to draw the reader’s attention to the change in hazard rate for growth rates beyond negative percent. This is all basically the same as the observation made earlier on house price growth rate that prepayment probability does not change as growth rates increase decreases beyond negative percent. Figure 57: Default Hazard Rate Across Time Under Different Income Drift Term 0.018 0.016 0.014 Income Growth Rate -10% Income Growth Rate -5% Income Growth Rate 0% Income Growth Rate 5% Income Growth Rate 10% Probabilities 0.012 0.01 0.008 0.006 0.004 0.002 0-11 12-23 23-35 36-47 48-59 60-71 72-83 84-95 96-107 108119 120131 132143 144155 156167 168179 180 Mor tgage Term (m onths) Note: Our initial analysis reveals marginal change in default rate due to the low volatility and low LTV ratio base case environment. We adjust some of the parameters to enhance the visualization of the simulated change in default probabilities. We set the house price volatility at 10 percent, the income volatility at 10 percent and LTV ratio at 90% in the above analysis. In our traditional fashion of analyzing hazard rates, we follow on to segregate the hazard rate into different time intervals in figure 56. The increase in prepayment hazard rate, as consistent with other sensitivity analysis of hazard rate across time, is generally concentrated within the first 36 months of the mortgage. Note that also there is no change in hazard rate across time when µ Y decreases beyond negative percent, a phenomenon that is consistent with our previous analysis. On the other hand, default hazard rates across time exhibit a similar pattern of change as that of house price volatilities (as shown in figure 57). Note that as well as being shifted upwards, the default hazard rate 119 distribution change begins to concentrate within the first 36 months of the mortgage as income growth rate declines. This is an obvious illustration of a spreading out effect of optimal default across time as we have mentioned earlier in the analysis of house price volatilities. Note that there is nothing absurd about having negative growth rates in which either house price would be expected to depreciate over time or income is expected to fall over time. We envision such effects to capture the effect of the notion of a depressed economy which either undergoes long periods of deflationary pressure or is persistently suffering from structural economic problems. A good example would be Japan which undergoes a 13-year period of deflation. We find that in a depressed economy, declining income is often accompanied by depreciating asset values. The overall effect from our combined analysis reveals that default becomes more attractive to borrower and prepayment becomes a more remote possibility. We caution, however, that it is naive to speak of the given percentage decease in µ Y and µ H as pure depression, since the precise effects of such a phenomenon would to be analyzed in a full model of the economy. In particular, we note that the inherent correlation structure between interest rates, house price and income would definitely change the outcome of our initial analysis. 120 Figure 58: The Distribution of Default Severities under Different Income Growth Rates 0.16 0.14 Income Growth Rate -10% Income Growth Rate -5% 0.12 Income Growth Rate 0% Probabilities 0.1 Income Growth Rate 5% Income Growth Rate 10% 0.08 0.06 0.04 0.02 0-0.025 0.0250.05 0.050.075 0.0750.1 0.10.125 0.1250.15 0.150.175 0.1750.2 0.20.225 0.2250.25 0.250.275 0.2750.3 0.30.325 0.3250.35 0.350.375 De fault Severity Levels In figure 58, we show the distribution of default severities for various income growth rates. Notice that µ Y affects the default severities in two ways. Firstly, the increase in µ Y dampens the distribution curve, causing its amplitude to decrease. Secondly, the peak of the curve illustrates a leftwards migration as µ Y increases. This implies that both the default severities and probabilities have both decreased as a result of µ Y increase. Given the increase in µ Y , the likelihood of ability-to-pay problem decreases and thus diminishing the role of default. However, if income follows a supermartingale process and as µ Y decreases, borrowers are substituting later terminations for earlier defaults. Coupling with fact that the amortization of mortgage increases the gap between H t and U t over time, the default severities as a result of earlier defaults increase as µ Y decreases further into the negative region. The effect of µ Y is also examined in the context of prepayment severities in figure 59. We expect prepayment to increase as µ Y increases given the borrower’s improving 121 ability-to-pay status over time enhance his/her ability to refinance. As our simulation reveals, the distribution curve shifts downwards and the tail of the curve moved towards the origin as µ Y increases. This agrees with the expectations we formed earlier where we argue that the effect of µ Y increase is to enhance the borrower’s ability to refinance. Figure 59: The Distribution of Prepayment Severities under Different Income Growth Rates 0.025 Income Growth Rate -10% 0.02 Income Growth Rate -5% Income Growth Rate 0% Probabilities Income Growth Rate 5% Income Growth Rate 10% 0.015 0.01 0.005 0-0.025 0.025-0.05 0.05-0.075 0.075-0.1 0.1-0.125 0.125-0.15 0.15-0.175 0.175-0.2 Prepayment Severity Levels Most banks in Singapore have a 1.5: year rule of thumb where they estimate that most mortgages will break even in 1.5 years and hence according to their calculation, they have to lock in the mortgage with a penalty for years to ensure profitability in their mortgage lending operation. Our simulation analysis illustrates that given a change in economic conditions, the first three-year default and prepayment will be most severely affected. We hereby provide theoretical evidence that lenders have to lock in the mortgage with penalty for three years to limit their default and prepayment losses in the face of changing economic environment. However, we caution that in face of high 122 volatilities, a 3-year penalty will not able to cover a lender’s termination losses as our analysis shows that the optimal default will tend to spread out into the subsequent years. 123 4.5 Practical and Theoretical Implications Practical: Mortgages should be accompanied with either a three-year prepayment penalty, lockout period or mortgage insurance. Our simulation analysis has provided the evidence that in the face of changing economic conditions, changes in default and prepayment probabilities are concentrated in the first years. Therefore, we caution that lenders will face the greatest risk in the first years after the origination of the mortgage. To limit the lender’s prepayment risk, the mortgage should be originated with either a year prepayment penalty or lockout period. Correspondingly, to limit default losses, lenders could consider mortgage insurance for the first years of the mortgage. Practical: Compared to FRM and ARM, PRM is a more ideal instrument for securitization given that PRM has the highest survival rate. Our comparative analysis of the three types of mortgages showed that PRM has the lowest default risk and the highest survival rate. In the case of securitization, the realized returns to the investors of mortgage-backed securities will be reduced by the effects of early terminations such as default and prepayment. Securities backed by a pool of PRMs would definitely offer better realized returns compared to that of ARM and FRM, as PRMs offers the lowest termination rate among the three types of mortgages. However, 124 the complex variations in mortgage terms of PRMs would be an obstacle for securitization pooling. Theoretical: Traditional valuation methods such as internal rate of return and net present value often undervalue mortgages and fail to account for the option-pricing characteristics of mortgages. Our simulation results have clearly shown that the omission to price implicit default and prepayment options causes the over-valuation of mortgage value. Traditional valuation methods such as internal rate of return and net present value have failed to capture such early termination decision-making process in their calculation. Therefore, a fundamental change in valuation methodology must be facilitated towards an option-based simulation approach to reflect more accurately the market value of mortgages. Theoretical: Monte Carlo approach is a more suitable pricing methodology for mortgages. Traditional dynamic programming techniques such as finite difference and binomial tree suffer from the problems of dimensionality and path-dependency. In this study, we have illustrated a technique (Least Square Monte Carlo Approach) that overcomes the two drawbacks. In addition, the technique is able to handle multiple stochastic variables and can be modified easily to reflect the complex variations in PRM. Therefore, the use of 125 this Monte Carlo technique would be ideal for pricing complex structure mortgages, like PRMs. 126 CHAPTER FIVE 5. CONCLUSIONS AND LIMITATIONS 5.1 Conclusions This study is motivated by the explosion of mortgage loan war in Singapore, which arises from the recent changes in housing and financing policies. In order to secure a larger market share of this sector, lenders are aggressively reducing promotional rates and coming up with a wide array of preferential rate mortgage packages to attract potential borrowers. For borrowers, the difference in value among the various types of mortgage packages remains hazy. The increased prevalence of PRMs demands attention to its valuation, comparison, risk assessment and implications. This study attempts to fulfill such motivations by providing a theoretical model to value and assess PRMs. From a theoretical perspective, the valuation of a preferential rate mortgage would require a pricing methodology that fulfills the following requirements. Firstly, the methodology must be flexible enough to accommodate the integration of fixed and floating coupon rate features in PRMs. Secondly; the methodology must be able to handle the path-dependence structure of the adjustable coupon rate feature in PRMs. Thirdly, the methodology must be able to capture the rational, forward-looking behavior and also the early termination decision-making process of borrowers. Lastly, the methodology must be able to handle multiple stochastic variables and is free from the “curse of 127 dimensionality”. We find that most traditional dynamic programming techniques in the literature such as finite difference or binomial tree method not fulfill all the above requirements. This provided the motivation to resort to the use of a forward-pricing method, the Least Square Monte Carlo approach of Longstaff and Schwartz to value preferential rate mortgages. This study adopts the view that a mortgage is just another financial contract and so, can be valued by an OPM. The decision to default or prepay is an option available to the borrower and exists only when it is in the borrower’s financial interests. Our modeling strategy in this study is that the default and prepayment decision is formulated as intertemporal optimization problem in a stochastic economy. Mortgage researchers often compared empirical results with predictions from theoretical options-pricing model (OPM). Several authors like Vandell (1995) have noted that the rates of termination predicted by the option theory are significantly higher than observed rates in the market. Consequently, the studies occasionally criticize OPMs when theoretical predictions not match up to empirical results. Some versions of OPMs used for comparison, however, are often only a strict form of the OPM, leaving many questions as to the validity of any over-generalized conclusions criticizing the usefulness of all OPMs. Our model contributes in this area of discussion by considering additional features like transaction costs, suboptimal termination, underwriting constraints and income-stress rules which will increase the realism, flexibility and adaptability of the model. 128 An traditional two-state variable OPM has no direct way of capturing the income and consumption determinants of mortgage termination. As an alternative to a pure optiontheoretic analysis of mortgage termination behaviour, we create a model using concepts from the credit-rationing and life-cycle-consumption literature. Large enough declines in income force borrowers to consider reducing housing expenses. They will prepay or default, depending on whether any housing equity remains. The model shifts the explanation of mortgage default from an option-theoretic unwillingness to pay the loan to a consumption-theoretic inability to pay. Expectations of interest rate and house prices drive borrower decision rules in the option-theoretic framework. Life-cycle consumption theory and mortgage institutional practices introduce a role for income and underwriting constraints to affect the exercise of default and prepayment options. We present the argument that default is driven by both equity and income considerations. There exists a threshold limit for exiting out of a mortgage contract, in which if income falls below the threshold limit, borrowers will make a choice between default and prepayment, based on equity considerations. This threshold limit, we posit, is peculiar to the borrower’s characteristics and is exogenously determined by his/her overall consumption behavior. We also further argue that income is not only a determinant in default, but also an important constraint in refinancing. By endogenously considering income constraints, we effectively restrict “loose” refinancing activity. The consequence of this is that, as we have in our numerical analysis, default and prepayment opportunities are weaken, bringing our model closer to realism. 129 The traditional assumption is that rational individuals default or prepay on their property only when it is in their financial interest to so. We alter this assumption by incorporating trigger events that induce individuals to prepay and default for personal reasons and unexplained events that enables individuals to continue their mortgage servicing when it is not in their financial interest to continue doing so. Such suboptimal default and prepayment is idiosyncratic to the particular borrower, as opposed to optimal default and prepayment. The research of Deng et al (2000) and Downing et al (2001), for example, show that significant borrower heterogeneity exists. A key point about OPMs is that personal characteristics of borrower (income, employment, status) are irrelevant. We deviate from such contention and seek to integrate borrower characteristics like income, consumption threshold level, job stability into the model. This enables us to discover the influence of borrower heterogeneity on termination behavior while simultaneously preserving prepayment and default financial decisions. By incorporating such termination events into the model, we seek not only to increase the realism of the model but also provide an avenue to incorporate specific borrower’s characteristics into the model. On top of using the setup of OPM to calculate values of default and prepayment, as is done in pervious literature, we have modified our original model to allow us calculate the probabilities of termination and corresponding the survival probabilities. Our premise is that this kind of information will be more useful to practitioners than the dollar value estimates of mortgages. OPM implicitly contains all the information necessary to determine the probability of default or prepayment in all possible situations. The paper 130 uses severity models to determine the credit risk of the lender. This paper goes beyond the standard operation of OPMs, to simulate the distribution of severities for prepayment and default that average up to the market cost of the lender’s liability. The point of this paper is that Least square Monte Carlo technique provides the means not only for calculating option values but also calculating probability distributions, thus improving the default and prepayment risk evaluations for the lender and mortgage investor. For a better understanding of risk profile of mortgages, the paper provides an extensive analysis of probabilities and severities of default and prepayment, building on the principles of OPMs. Our comparative analyses of mortgage contracts indicate that FRM ranks the highest in terms of prepayment risk, followed by PRM and lastly pure ARM. In addition, PRMs rank the lowest in terms of default risk, followed by FRM and lastly ARM. PRMs also rank the highest in terms of survival rate, followed by ARM and lastly FRM. We also present the evidence that such ranking order relationship is stable across different housing market conditions. Our comparison of PRM with FRM and pure ARM reveals that PRM has the lowest default risk and highest survival rate among the three types of mortgages. From our above reasoning, we hence argue the PRMs are a low risk asset class for lenders (as compared to FRMs and ARMs) and would be an ideal instrument for securitization. Early termination of mortgages tends to reduce the realized returns to the investors of mortgage-backed securities and thus mortgages that have the highest survival rates are often highly valued by securitization originators. PRMs, in this respect, would be ideal asset for securitization given that it provides a lower risk profile than ARM and 131 FRM. However, the major obstacle here is that PRMs lacks market standardization in mortgage terms for securitization pooling. 5.2 Contributions of Study 1. We propose a pricing model in a competing risk framework that is able to accommodate the integration of floating and fixed coupon rate feature. 2. Most types of numerical techniques in mortgage pricing suffer from one or more drawbacks such as inability to extend to multiple stochastic factors, the curse of dimensionality, the inability to integrate rational decision-making and the inability to handle path-dependency. The contribution of our study is that our proposed model overcomes these drawbacks. 3. Our study proposes a four factor mortgage theoretic option pricing model which incorporates a household income process and a two factor term structure process to negate the ruthless default conditions and also to enhance the characterization of long term mortgage rate processes. 4. Our model allows for borrower heterogeneity and modeling of various fictions like transactions, suboptimal termination and suboptimal nontermination. 5. Our model allows for the endogenization of underwriting guidelines which is useful for evaluating policy changes related to the housing and mortgage markets. 6. Our model, besides pricing mortgages, is capable of generating risk profile of mortgages in terms of probabilities and severities of termination. 132 5.3 Limitation of Study 1. Suboptimal default, prepayment and nontermination are assumed to follow a Poisson process that is time-invariant during the lifespan of the mortgage. No empirical research has been conducted on this aspect to support our assumptions. Our analysis has shown that the results are rather sensitive to the formulation of these suboptimal processes. Therefore, if the true underlying nature of these suboptimal processes differs a lot from what we assumed, the simulated results could be quite different. 2. Due to the non-existence of FRMs in Singapore, we had to create a hypothetical FRM in place using equivalent IRR approach for our analysis. This approach is rather weak as the derived contract rates are highly hypothetical based on our own derivation. 5.4 Recommendations for Further Study 1. In Singapore, the mortgagee’s Central Provident Fund (CPF) contributions can be used to pay off part or all of the mortgage payments. CPF contributions inherently carry a different opportunity cost of capital as compared to equity. It is worth exploring how the changes in CPF policies will affect default and prepayment activities. 2. Suboptimal default, prepayment and nontermination are relatively new concepts in the literature. It is worthwhile to conduct further empirical research to 133 understand the nature of these processes. This will provide the appropriate specifications to model them in a theoretical construct. 3. The model could also be modified to price and analyze mortgage-backed securities. 4. In reality, when borrowers move for income reasons, the marginal transaction cost of prepaying and default is lower because moving is certain. More studies could be done to establish formal relationships of transaction costs with different trigger events and different borrower characteristics. 134 [...]... Keenan, and Muller (199 3a) ; Kau, Keenan and Kim (2001); Kau and Keenan (1999); and Schwartz and Torous (1992) began to integrate mortgage insurance as part of the overall mortgage valuation framework The treatment of mortgage insurance can be done in two ways: as an upfront lump sum payment or as part of the contract rate that determines monthly payments Most researchers adopted the former approach 16... (1984) have considered GPMs and Kim (1987) analyzes PLAMs Another less common form of residential mortgages, which is unique to Singapore is the preferential rate mortgages (PRMs) PRMs are essentially ARMs that are served with a promotional rate within a promotional term of three to six years The promotional rate may come in two forms, either as a below-themarket fixed contract rate or as a contract rate. ..value of default is less in the presence of prepayment than in its absence, just as the value of prepayment is less in the presence of default than in its absence 2.1 Pricing Mortgages as Contingent Claims Traditional valuation in the world of certainty is straightforward: that is to do a present value calculation In the world of uncertainty, valuation of assets with early termination features... explicitly analyzing ARMs and other variable rate contracts includes Buser, Hendershott, and Sanders (1985); Cox, Ingersoll, and Ross (1980); Findlay and Capozza (1977); Kau et al (1985, 1990b, 1993b); and Schwartz and Torous (1991) A point worth noting is that the problem of pathdependency is often associated with ARMs Unlike fixed -rate mortgages, ARMs have terms that depend on past interest rates This causes... Types of Mortgage Contract The most common type of residential mortgages in US is the fixed rate mortgages which have a fixed contract rate and a fixed monthly payment From an option-theoretic viewpoint, several papers like Buser and Hendershott (1984), Epperson et al (1985), Kau et al (1992,1995), and Pozdena and Iben (1984) explicitly considerd such fixed rate mortgages Adjustable -rate mortgages (ARMs),... spot rate, γ the mean reversion coefficient, θ the trend rate, σ r the volatility parameter and dz r the Wiener process The term structure is assumed to revert towards a trend rate θ (at a rate dictated by γ ) and it always avoids the negative interest rate condition As interest rate is not a directly tradable asset, in order to achieve riskneutral pricing, we assume either that the Local Expectations... a floating rate The numerous and complex variations in PRMs structure would warrant a robust evaluation and comparison framework for potential borrowers The basic question of how to evaluate and compare PRMs is essentially a question of PRM valuation By appealing to option pricing literature in general, this study attempts to develop a model for such purpose Valuation of both fixed rate mortgages (FRMs)... Clément et al (2002) and Egloff and Min-Oo (2002) prove the almost sure convergence of the complete least square Monte Carlo algorithm for a fixed finite set of basis functions and also establish a type of central limit theorem for the rate of convergence of the Monte Carlo method, thus proving its normalized error is asymptotically Gaussian A detailed analysis of LSM is also carried recently by Stentoft... the other hand, are mortgages that have a contract rate that is adjusted periodically to reflect prevailing interest rates and as a result, subject borrowers to the variability in payments Most ARMs in US would have features like lifetime caps, lifetime floors, periodic caps, periodic floors and teaser rates For a comprehensive review of ARM features, see Schwartz and Torous (1991) Theoretical models... (FRMs) and adjustable rate mortgages (ARMs) has been well developed both theoretically and empirically in the literature PRMs, a unique class of mortgages, on the other hand, lack such theoretical and empirical development Following the seminal works of Black and Scholes (1973) and Merton(1973), the optiontheoretic approach to pricing mortgages offers a new insight into opportunities of prepay and default . fixed rate mortgages. Adjustable -rate mortgages (ARMs), on the other hand, are mortgages that have a contract rate that is adjusted periodically to reflect prevailing interest rates and as a result,. Pricing Mortgages as Contingent Claims Traditional valuation in the world of certainty is straightforward: that is to do a present value calculation. In the world of uncertainty, valuation of assets. lacks such a framework for the benefit of the mortgagor and mortgagee to facilitate comparison and pricing. In addition, as a result 1 Preferential Rate Mortgages (PRMs) are adjustable rate