Option-based Models Research Articles

Modeling Behavioral Risk

Contracts with embedded prepayment/extension options are subject to behavioral risk, due to the unpredictable exercise strategy followed by the option holder. Empirical data show that, in many situations and for different reasons, investors do not act purely on the strength of financial convenience and do not take full advantage of the option owned. When seen from the viewpoint of the option seller, such behavior results in a lower option value and an additional source of uncertainty in future cash flows. In this paper, we propose a general framework to model behavioral risk by exploiting a parallel with credit risk modeling. Early redemption probabilities are assimilated to default probabilities and investor decisions to default events. Our approach is micro-structural, meaning that the aggregate prepayment rate derives from individual decisions. It also combines some features of intensity-based and option-based models, which have been reported in literature.

A General Option Valuation Approach to Discount for Lack of Marketability

A general option-based approach to estimating the discount for lack of marketability is offered. It is general enough to capture maturity, volatility, hedging availability, and investor skill, as well as other important factors. The model is shown to contain several option-based models as special cases. The model also contains two weighting variables that provide valuation professionals much needed flexibility in addressing the unique challenges of each nonmarketable valuation assignment. Selected prior empirical results are reinterpreted with this approach.

Integration of Accounting-Based and Option-Based Models to Predict Construction Contractor Default

This paper aims to predict construction contractor default, which is excluded by most extant studies, due to the distinct characteristics of construction industry. Default predicting models developed in past literatures are mostly built by accounting information, yet accounting sheets have innate flaws. To calculate default probability, several recent studies applied the option pricing theory, which presumes that the stock market is efficient. This presumption isn't always true in real life. In this paper, a hybrid model is proposed. It combines information from both models by inputting the default probability from the option-based model into the accounting-based model. As the measure of models' predicting performance, the Area Under the receiver operating characteristic Curve (AUC) is used. Empirical results show that the hybrid model (AUC: 0.8732) outperforms both the accounting-based model (AUC: 0.7519) and the option-based model (AUC: 0.8581). This result shows that accounting or stock market information alone is not sufficient to explain real-world behavior. It is suggested that the hybrid model be used as an alternative prediction model of construction contractor default.

A note on applying option pricing theory to emerging mortgage and mortgage-backed securities markets

Option-based models have been the dominant paradigm for researches on the risks and pricing of mortgages and Mortgage-Backed Securities (MBS) in the USA. However, the adaptability and flexibility of option-based models in the emerging mortgage markets has been obviously neglected. This study provides the first analysis of the potential strengths and weaknesses of application of the option pricing theory to emerging markets with referring to both theoretical and empirical literatures. This study finds that the mortgage type, the attitude of mortgagees to risk and the institutional features are the key determinants of success of application of the option pricing theory to emerging mortgage and MBS markets. The option pricing literature in finance has been extended to study the risks and pricing of mortgages and MBS in the USA over the last three decades. However, given the robust and rapid growth of emerging mortgage and mortgage-related capital markets, there is surprisingly little known about to what extent the option pricing theory can be applied to the emerging mortgage and MBS markets in the global arena. The purpose of this study is to fill this gap by analysing the potential strengths and weaknesses of application of the option pricing models to emerging markets with specifically referring to both theoretical and empirical literatures.

Default risk and equity returns: Australian evidence

We test whether default risk is related to equity returns using the Fama and MacBeth [Fama, E.F., MacBeth, J., 1973. Risk, return, and equilibrium: empirical tests. Journal of Political Economy 81, 607–636.] regression framework. The proxy we use for default risk is the default probability obtained from option-based models. Our findings show that default probability is negatively related to returns. While we find that size and book-to-market are related to default risk, the ability of these variables to explain cross-sectional variation in returns is not because they are proxying default risk. Further, our evidence suggests that the negative relationship between default probability and returns is not due to a leverage, volatility or momentum effect.

Taxation of Risky Investment and Paradoxical Investor Behavior

Under uncertainty and irreversibly, real option-based models are widely accepted for assessing investment projects. So far the existing post-tax analyzes do not provide a general analytical description of investor reactions towards profit tax rate changes. This paper sets out to fill part of the void. We implement a simple tax system and focus on risky capital market investment and an option to wait. Taxes affect risk-free and risky capital market investment asymmetrically and hence cause distortions. We analytically identify a set of neutral tax rates (tax regimes) that preserve the critical post-tax investment threshold in case of tax rate changes as well as general normal and paradoxical settings. Unlike for other tax paradox neither depreciation rules nor loss offset restrictions are responsible for the observed paradoxical reaction. Identifying normal and paradoxical tax regimes can be regarded as a first step to a generalized description of tax effects under uncertainty, both for individual project evaluation as well as for understanding tax effects on an aggregate level.

Investigating the Performance of Alternative Default-Risk Models: Option-Based Versus Accounting-Based Approaches

In this paper we evaluate the performance of three alternate default-risk models, seeking to find that measure which performs best, using a comprehensive sample drawn from the Australian equities market. The first two models are option-based models and are derived from Merton's (1974) insight that equity can be viewed as a call option on a firm's assets. In the first model, equity is modelled as a standard call option. In the second model, equity is modelled as a path-dependent barrier option. The third model is created using accounting ratios and is similar to Altman's (1968) Z-Score. To assess which of the models is superior, we consider variations of each model and then rely on prediction-oriented tests that focus on whether a firm subsequently defaults. Our results show that the option-based models clearly outperform their accounting ratio counterparts. Furthermore, our analysis suggests that the option-based models are very successful at ranking firms by default probability. It is noteworthy that the performances of the option-based models are difficult to distinguish from each other.

Commercial mortgage underwriting: How well do lenders manage the risks?

Loan-to-value ratio and debt service coverage ratios have long been viewed as the two most important quantitative measures of the default risk of commercial mortgages. Option-based models of default provide strong theoretic support for the importance of original loan-to-value ratio. The same theoretical predictions have found strong empirical support in residential single-family mortgage analyses. However, recent empirical studies of commercial mortgage default have raised questions about the role of loan-to-value ratio in assessing the riskiness of commercial mortgages. These studies generally either find no relationship or a puzzling negative relationship between loan-to-value ratio and default. This paper uses a very large database of commercial loan histories to thoroughly investigate this issue. It finds strong evidence that loan-to-value and debt service coverage ratios are endogenous to the underwriting process. Lenders react to other—unmeasured—risk factors with credit rationing and pricing. As a result, unusually low loan-to-value ratio loans appear to have above average risk in other dimensions and their default probabilities are equal to or higher than average. The results show that the pricing spread that lenders establish as part of the underwriting process serves as an excellent summary measure of the riskiness of the loan. A test of lenders’ ability to appropriately price loan-to-value risk finds that, while there is some unpriced effect of loan-to-value ratio after controlling for the lender’s pricing, introducing lender pricing into the model removes the otherwise puzzling negative loan-to-value and default relationship previously observed in the literature.

Spatial Heterogeneity in Mortgage Terminations by Refinance, Sale and Default

This paper investigates the impact of spatially correlated unobservable variables on the refinancing, selling, and default decisions of mortgage borrowers. Virtually the entire mortgage literature acknowledges that borrower specific characteristics, such as culture, education, or access to information, play an important role in the mortgage termination decisions. While we do not observe these variables directly, we note that borrowers of similar background tend to cluster together in neighborhoods. We propose a method to take advantage of this information and reconcile the theoretical option-based models of mortgage terminations with the empirical experience of mortgage refinancing, sale, and default. Specifically, we estimate a competing risks hazard model with random effect using a three-stage maximum likelihood estimation (3SMLE) approach with space-varying coefficient method (SVC) to modify the covariance structure according to the spatial distribution of the observations. Beyond a significant improvement of the model performance, this yields a number of insightful implications for mortgage termination behavior. For instance, borrowers of the affluent West Side of Los Angeles County both refinance and move at a higher rate than predicted by the standard maximum likelihood estimation method. At the same time, borrowers from some lower-valued neighborhoods tend to stay longer than expected with their mortgages and properties. Such findings have direct implications for mortgage pricing and have the potential to ultimately improve the equity and efficiency of the lending markets.

Commercial Mortgage Underwriting: How Well Do Lenders Manage the Risks?

Loan-to-value ratio and debt service coverage ratios have long been viewed as the two important quantitative measures of the default risk of commercial mortgages. Option-based models of default provide strong theoretic support for the importance of original loan-to-value ratio. The same theoretical predictions have found strong empirical support in residential single-family mortgage analyses. However, recent empirical studies of commercial mortgage default have raised questions about the role of loan-to-value ratio in assessing the riskiness of commercial mortgages. These studies generally either find no relationship or a puzzling negative relationship between loan-to-value ratio and default. In this paper, we use a very large data base of commercial loan histories to thoroughly investigate this issue. We find strong evidence that loan-to-value ratio (and debt service coverage ratio) is endogenous to the underwriting process. Lenders react to other (unmeasured) risk factors by a combination of credit rationing (lowering the loan amount) and pricing. As a result, unusually low loan-to-value ratio loans appear to have above average risk in other dimensions and their default probabilities are equal to or higher than average. We find that the pricing spread that lenders establish as part of the underwriting process serves as an excellent summary measure of the riskiness of the loan. We test the effectiveness of lenders' ability to appropriately price loan-to-value risk and find that, on average, there is no unpriced effect of loan-to-value ratio after controlling for the lender's pricing.

Effects of Noise on Optimal Exercise Decisions: The Case of Risky Debt Secured by Renewable Lease Income

This paper considers the valuation and default exercise policy of risky coupon debt that is secured by a lease-encumbered noisy real asset. For parameter values used in our analysis, asset value noise is shown to reduce the value of waiting to default. Moreover, the borrower is shown to delay default exercise until the noisy signal of asset value is far into-the-money. This latter finding provides an information-based explanation for the apparent under-exercise of the mortgage default option that has been observed in the literature. An implication of this finding is that, if the claimholder recognizes that noise exists, but the empiricist—who is trying to compare observed exercise policy with that predicted by a noiseless model of asset prices—does not, a “sub-optimal” exercise policy may be inferred when in fact the policy is rational given the information available. This explanation is consistent with evidence from mortgage default studies as to why the observed default exercise boundary is lower than that predicted by standard theoretical option-based models.

REAL OPTIONS: STATE OF THE PRACTICE

In the mid‐1980s, financial economists began building option‐based models to value corporate investments in real assets, laying the foundation for an extensive academic literature in this area. The 1990s saw several books, numerous conferences, and many articles aimed at corporate practitioners, who began to experiment with these techniques. Now, as we approach the end of 2001, the real options approach to valuing real investments has established a solid, albeit limited, foothold in the corporate world.Based on their recent interviews with 39 individuals from 34 companies in seven different industries, the authors of this article attempt to answer the question, “How is real options being practiced, and what impact is it having in the corporate setting?” The article identifies three main corporate uses of real options—as a strategic way of thinking, an analytical valuation tool, and an organization‐wide process for evaluating, monitoring, and managing capital investments. For example, in some companies, real options is used as an input into an M&A process in which rigorous numerical analysis plays only a small role. In such cases, real options contributes as a qualitative way of thinking, with little formality either in terms of analytical rigor or organizational procedure. In other firms, real options is used in a commodity trading environment where options are clearly specified in contracts and simply need to be valued. In this case, real options functions as an analytical tool, though generally only in specialized areas of the firm and not on an organization‐wide basis. In still other companies, real options is used in a technology or R&D context where the firm's success is driven by identifying and managing potential sources of flexibility. In such cases, real options functions as an organization‐wide process with both a broad conceptual and analytical core.The companies that have shown the greatest interest in real options generally operate in industries where large investments with uncertain returns are commonplace, such as oil and gas, and life sciences. Major applications include the evaluation of exploration and production investments in oil and gas firms, generation plant investments in power firms, R&D portfolios in pharmaceutical and biotech firms, and technology investment portfolios in high‐tech firms.While the approaches to implementation are quite varied, there appears to be a common path to the successful adoption of real options. The key steps of the adoption process are: (1) conducting pilot projects; (2) getting buy‐in from senior‐level and rank‐and‐file managers; (3) codifying real options through expert working groups, specialist training, and customization; and (4) institutionalizing and integrating real options firm‐wide. After citing best practices for each of these four steps, the authors close by predicting that a “network” effect and acceptance by Wall Street will serve as catalysts for more widespread corporate use of real options.

Determinants of Multifamily Mortgage Default

Option-based models of mortgage default posit that the central measure of default risk is the loan-to-value (LVT) ratio. We argue, however, that an unrecognized problem with extending the basic option model to exisiting multifamily and commercial mortgages is that key variables in the option model are endogenous to the loan origination and property sale process. This endogeneity implies, amoung other things, that no emperical relation may be observed between default and LTV. This is because lenders may require lower LTVs in order to mitigate risk so mortgages with low and moderate LTVs may be as likely to default as those with high LTVs. Mindful of this risk endogeneity and its emperical implications, we examine the default experience of 9,639 multifamily mortgage loans securitized by the Resolution Trust Corporation (RTC) and the Federal Deposit Insurance Corporation (FDIC) during the period 1991-1996. The extensive nature of the data supports multivariate analysis of default incidence in a number of respects not possible in previous studies.

Mortgage Default with Asymmetric Information

This paper analyzes mortgage-market equilibrium when borrower default costs are private information. By applying the approach of Rothschild and Stiglitz (1976), it is shown that asymmetric information regarding default costs distorts the contract choices available in the mortgage market, preventing safe borrowers (those with high default costs) from fully satisfying their demand for mortgage debt. Large loans are available for a substantial interest-rate premium, but only risky borrowers find this premium worth paying. The paper builds on an empirical literature designed to test the ruthless-default principle from option-based models of mortgage pricing. That literature provides evidence against ruthless behavior, suggesting that default costs play an important role in borrower decisions. The paper takes a further step by arguing that such costs are private information, which has important implications for market equilibrium.

The Role of Uncertainty in Investment: An Examination of Competing Investment Models Using Commercial Real Estate Data

Neoclassical investment decision criteria suggest that only the systematic component of total uncertainty affects the rate of investment, as channeled through built asset price. Alternatively, option-based investment models suggest a direct role for total uncertainty in investment decision making. To sort out uncertainty's role in investment, we specify and empirically estimate a structural model of asset market equilibrium. Commercial real estate time series data with two distinct measures of asset price and uncertainty are used to assess the competing investment models. Empirical results generally favor predictions of the option-based model, and hence suggest that irreversibility and delay are important considerations to investors. Our findings also have implications for macroeconomic policy and for forecasts of cyclical investment activity.

Deficiency Judgments and the Exercise of the Default Option in Home Mortgage Loans

IN recent years it has become common to treat mortgagor default as an exercise of a put option. This approach has the advantage of focusing attention on rational exercise of an implicit option, an important focus if mortgage loans are to be adequately valued by the option pricing model (OPM). The no-arbitrage-profit assumption underlying the OPM, however, requires all the attributes of perfect markets, including zero transaction costs. Among other things, the absence of transaction costs implies that lenders and mortgage insurers have no access to collateral other than the pledged real estate. Consequently, on the one hand, option-based models of default downplay the importance of transaction costs in general and dismiss the possibility of enforceable personal covenants in particular.' On the other hand, the poor predictive value of empirical models2 has prompted some schol-

An Exposition of the Implications of Limited Liability and Asymmetric Taxes for Property-Liability Insurance

ABSTRACT This article elaborates upon the intuition underlying Doherty and Garven's (1986) option pricing model and extends its basic results to a further consideration of the implications of limited liability and asymmetric taxes for pricing and incentives in property-liability insurance. When compared with CAPM-based models of the insurer, a number of important insights emerge. First, the option pricing framework is shown to encompass the CAPM framework as a special case and may help to explain a number of empirical phenomena. Second, the option pricing framework is used to develop a risk hypothesis which suggests that limited liability and asymmetric taxes provide mutuals with greater disincentives for riskbearing than stock companies, even in the absence of owner/manager conflicts. Although the property-liability insurance industry has been subject to price regulation for many years, researches have only recently derived valuation formulas for property-liability insurance firms. To date, the most promising approaches apply financial theories such as the capital asset pricing model (CAPM) (see Biger and Kahane, 1978; Fairley, 1979; Hill, 1979; Hill and Modigliani, 1987; and Myers and Cohn, 1987) and the option pricing model (see Doherty and Garven, 1986; Cummins, 1988b; and Derrig, 1989). Although details vary, these models are generally organized around the principle that the rate of underwriting profit must be set so as to produce a fair, or competitive rate of return on equity.(1) In spite of their common origins, CAPM and option-based insurance pricing models produce substantially different predictions concerning pricing and incentives for property-liability insurance. It will be shown that these differences are primarily due to the manner in which the effects of insolvency and taxes are modeled. Essentially, CAPM-based models implicitly assume that shareholders have unlimited liability, whereas option-based models assume that shareholders' liability is limited. Similarly, by assuming that losses are rebated at the same rate at which gains are taxed, CAPM-based models effectively assign unlimited liability to the government, whereas option-based models limit the government's liability by assuming that gains and losses are taxed in an asymmetric fashion. This article elaborates upon the intuition underlying Doherty and Garven's (1986) option pricing model and extends its basic results to a further consideration of the implications of limited liability and asymmetric taxes for pricing and incentives in property-liability insurance. This is accomplished by comparing and contrasting option-based with CAPM-based models of the insurance firm. This analysis yields a number of important insights, such as the fact that the option pricing framework encompasses the CAPM framework as a special case. The option pricing model also has several practical advantages over the CAPM. For example, it is not plagued by the CAPM's well-known parameter estimation problems; indeed, it may help to explain the causes of these problems.(2) The option pricing model also provides an explicit linkage between fair return and the risks of insolvency and tax shield underutilization, whereas the CAPM totally ignores these effects. The option pricing model also calls attention to some important incentive effects concerning risk-bearing that are not captured by the CAPM. Under the CAPM, asset and liability is not particularly important so long as these claims are priced to yield appropriate risk-adjusted rates of return. However, under the option pricing model, the extent to which firms will seek to increase or avoid through their investment and underwriting policy choices depends upon the likelihood of being taxed or becoming insolvent. Consequently, the application of the option pricing framework makes it possible to develop a risk hypothesis which predicts that mutual insurers will seek less exposure to than stock companies. …

The option valuation approach to mortgage pricing

The analysis of mortgage securities has made significant advances in the last few years. Prepayment forecasting is much improved and price-yield methodologies have been standardized. Development of techniques known as “option-based pricing models” has recently provided an important new tool for evaluating mortgage instruments.