住房抵押贷款支持证券定价模型的发展与启示

住房抵押贷款证券化发行的住房抵押贷款支持证券包含提前偿还风险和违约风险两个期权,这使得其定价要比一般债券的定价复杂得多。而我国的住房抵押贷款证券化又有着不同证券化发达国家的特点,因此研究国外定价模型的适用情景和发展对我国的实践是非常必要的。本文旨在沿着住房抵押贷款支持证券定价理论结构化和简约化模型两条主要线索的发展,对该领域的最新研究成果进行介绍和评价,并得出和我国住房抵押贷款证券化实践相关的启示。     

PREPAYMENT RISK AND THE DURATION OF DEFAULT-FREE MORTGAGE-BACKED SECURITIES

The conventional duration measure for mortgage-backed pass-through securities assumes that the prepayment rate is invariant to changes in market interest rates. In this paper, the conventional duration is modified to take into account the interest-rate sensitivity of mortgage prepayments. Including interest rate sensitivity is shown to reduce substantially the duration of a mortgage-backed pass-through security when the current mortgage rate is less than the contract rate.     

Performance based mortgage-backed securities indexing

The traditional approaches to indexing first developed for equities and then adapted to bonds are not effective for mortgage-backed securities. This paper details a new technique for indexing portfolios of mortgage-backed securities which rectifies the deficiencies of the older cellular method. By focusing on the performance characteristics of the bonds adjusted for their embedded options, we at once simplify the process of portfolio selection and increase the accuracy of performance tracking.     

Mortgage Termination: An Empirical Hazard Model with a Stochastic Term Structure

Pricing for mortgage and mortgage-backed securities is complicated due to the stochastic and interdependent nature of prepayment and default risks. This paper presents a unified economic model of the contingent claims and competing risks of mortgage termination by prepayment and default. I adopt a proportional hazard framework to analyze these competing and interdependent risks in a model with time-varying covariates. The paper incorporates a stochastic interest rate model into the hazard function for prepayment. The empirical results reported in the paper provide new evidence about the ruthlessness of default and prepayment behavior and the sensitivity of these decisions to demographic as well as financial phenomena. The results also illustrate that evaluating the interest rate contingent claims with a stochastic term structure has effects on predicting not only the mortgage prepayment behavior but also the mortgage default behavior.     

PRICING CURRENCY OPTIONS UNDER STOCHASTIC INTEREST RATES AND JUMP‐DIFFUSION PROCESSES

We investigate the effects of stochastic interest rates and jumps in the spot exchange rate on the pricing of currency futures, forwards, and futures options. The proposed model extends Bates's model by allowing both the domestic and foreign interest rates to move around randomly, in a generalized Vasicek term‐structure framework. Numerical examples show that the model prices of European currency futures options are similar to those given by Bates's and Black's models in the absence of jumps and when the volatilities of the domestic and foreign interest rates and futures price are negligible. Changes in these volatilities affect the futures options prices. Bates's and Black's models underprice the European currency futures options in both the presence and the absence of jumps. The mispricing increases with the volatilities of interest rates and futures prices. JEL classification: G13     

New No-arbitrage Conditions and the Term Structure of Interest Rate Futures

Interest rate futures are basic securities and at the same time highly liquid traded objects. Despite this observation, most models of the term structure of interest rate assume forward rates as primary elements. The processes of futures prices are therefore endogenously determined in these models. In addition, in these models hedging strategies are based on forward and/or spot contracts and only to a limited extent on futures contracts. Inspired by the market model approach of forward rates by Miltersen, Sandmann, and Sondermann (J Finance 52(1); 409–430, 1997), the starting point of this paper is a model of futures prices. Using, as the input to the model, the prices of futures on interest related assets new no-arbitrage restrictions on the volatility structure are derived. Moreover, these restrictions turn out to prevent an application of a market model based on futures prices.     

Intermarket efficiency: An application of interbattery APT to mortgage-backed securities

Increasing popularity of investments in mortgage-backed securities has led to closer integration of the mortgage market into traditional capital markets. Using monthly returns during 1982–1988 for common stocks, Treasury bonds and GNMA and FHLMC mortgage-backed securities, the interbattery factor analytic Arbitrage Pricing Theory of (Cho, 1984) is used to test five hypotheses for intramarket and intermarket integration. Results indicate that three to five common factors are found within the same security market, while only one to three factors are found common between different markets.The APT could not be rejected within the same security market, but was rejected in most intermarket comparisons. While risk-free rates are found to differ between markets, the risk premium tests are conclusive indicators of integration. Our results support claims that the stock, bond, and the mortgage-backed securities markets are integrated.     

Are interest rate options important for the assessment of interest rate risk?

Fixed income options contain substantial information on the price of interest rate volatility risk. In this paper, we ask if those options will also provide information related to other moments of the objective distribution of interest rates. Based on dynamic term structure models within the class of affine models, we find that interest rate options are useful for the identification of interest rate quantiles. Two three-factor models are adopted and their adequacy to estimate Value at Risk of zero-coupon bonds is tested. We find significant difference on the quantitative assessment of risk when options are (or not) included in the estimation process of each of these dynamic models. Statistical backtests indicate that bond estimated risk is clearly more adequate when options are adopted, although not yet completely satisfactory.     

Mortgage convexity

Most home mortgages in the United States are fixed-rate loans with an embedded prepayment option. When long-term rates decline, the effective duration of mortgage-backed securities (MBS) falls due to heightened refinancing expectations. I show that these changes in MBS duration function as large-scale shocks to the quantity of interest rate risk that must be borne by professional bond investors. I develop a simple model in which the risk tolerance of bond investors is limited in the short run, so these fluctuations in MBS duration generate significant variation in bond risk premia. Specifically, bond risk premia are high when aggregate MBS duration is high. The model offers an explanation for why long-term rates could appear to be excessively sensitive to movements in short rates and explains how changes in MBS duration act as a positive-feedback mechanism that amplifies interest rate volatility. I find strong support for these predictions in the time series of US government bond returns.     

Valuation of GNMA Mortgage-Backed Securities

GNMA mortgage-backed pass-through securities are supported by pools of amortizing, callable loans. Additionally, mortgagors often prepay their loans when the market interest rate is above the coupon rate of their loans. This paper develops a model for pricing GNMA securities and uses it to examine the impact of the amortization, call, and prepayment features on the prices, risks and expected returns of GNMA's. The amortization and prepayment features each have a positive effect on price, while the call feature has a negative impact. All three features reduce a GNMA security's interest rate risk and, consequently, its expected return.     

The price of a smile: hedging and spanning in option markets

The volatility smile changed drastically around the crash of1987, and new option pricing models have been proposed to accommodatethat change. Deterministic volatility models allow for moreflexible volatility surfaces but refrain from introducing additionalrisk factors. Thus, options are still redundant securities.Alternatively, stochastic models introduce additional risk factors,and options are then needed for spanning of the pricing kernel.We develop a statistical test based on this difference in spanning.Using daily S&P 500 index options data from 1986-1995, ourtests suggest that both in- and out-of-the-money options areneeded for spanning. The findings are inconsistent with deterministicvolatility models but are consistent with stochastic modelsthat incorporate additional priced risk factors, such as stochasticvolatility, interest rates, or jumps.     

Rational Prepayments and the Valuation of Collateralized Mortgage Obligations

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

GSEs,Mortgage Rates,and Secondary Market Activities

Fannie Mae and Freddie Mac are government-sponsored enterprises (GSEs) that securitize mortgages and issue mortgage-backed securities (MBS). In addition, the GSEs are active participants in the secondary mortgage market on behalf of their own investment portfolios. Because these portfolios have grown quite large, portfolio purchases (in addition to MBS issuance) are often thought to be an important force in the mortgage market. Using monthly data from 1993 to 2005 we estimate a VAR model of the relationship between GSE secondary market activities and mortgage interest rate spreads. We find that GSE portfolio purchases have no significant effects on either primary or secondary mortgage rate spreads. Further, we examine GSE activities and mortgage rate spreads in the wake of the 1998 debt crisis, and find that GSE portfolio purchases did little to affect mortgage rates. This empirical finding is robust to alternative identification assumptions and to alternative model and variable specifications.      

Interest Rate Futures Options and Interest Rate Options

This paper derives pricing models of interest rate options and interest rate futures options. The models utilize the arbitrage-free interest rate movements model of Ho and Lee. In their model, they take the initial term structure as given, and for the subsequent periods, they only require that the bond prices move relative to each other in an arbitrage-free manner. Viewing the interest rate options as contingent claims to the underlying bonds, we derive the closed-form solutions to the options. Since these models are sufficiently simple, they can be used to investigate empirically the pricing of bond options. We also empirically examine the pricing of Eurodollar futures options. The results show that the model has significant explanatory power and, on average, has smaller estimation errors than Black's model. The results suggest that the model can be used to price options relative to each other, even though they may have different expiration dates and strike prices.     

THE SURVIVAL ZONE FOR A BOND WITH BOTH CALL AND PUT OPTIONS EMBEDDED

We present a numerical method to price bonds that have multiple embedded options with an emphasis on the case with both long call and short put options. The valuation framework is a one-factor model for the term structure of interest rates, where the instantaneous interest rate is allowed to follow a fairly general stochastic process. The equilibrium interest rates that define the free boundaries for the embedded call and put options are given. We demonstrate the survival zone within which a bond with both long call and short put options remains afloat. We show that even moderate levels of transaction costs can have a significant effect on exercise of options.     

Pricing Commodity Spread Options with Stochastic Term Structure of Convenience Yields and Interest Rates

The purpose of this research is to provide a valuation formula for commodity spread options. Commodity spread options are options written on the difference of the prices (spread) of two commodities. From the aspect of commodity contingent claims, it is considered that commodity spread options are difficult to evaluate with accuracy because of the existence of the convenience yield. Hence, the model of the convenience yield is the key factor to price commodity spread options. We use the concept of future convenience yields to develop the model that enriches the stochastic behavior of convenience yield. We also introduce Heath-Jarrow-Morton interest rate model to the valuation framework. This general model not only captures the mean reverting feature of the convenience yield, but also allows us to handle a very wide range of shape that the term structure of convenience yield can take. Therefore our model provides various types of models. The numerical analysis presented in this paper provides some unique features of commodity spread options in contrast to normal options. These characteristics have never been addressed in previous studies. Moreover, it suggests that the existing model overprice commodity spread options through neglecting the effect of interest rates.     

A path-dependent approach to security valuation with application to interest rate contingent claims

The last two decades have witnessed a tremendous growth in the volume of assets and liabilities whose cash flows depend, in a variety of ways, on the path of interest rates. Some of these, including floating-rate notes and swap agreements, contractually base cash flows on current and past interest rates and contain caps, floors, and other, more complex features. Others, including mortgages, many corporate bonds, and time deposits, are fixed-rate instruments that contain embedded options, such as those to prepay, call, or withdrawal. The irregular exercise of these options causes cash flows to vary as time proceeds and interest rates rise or fall. This paper develops a state-contingent claims technique for valuing such securities. It is derived from the option-based model of Breeden and Litzenberger (1978) using the transition matrix approach of Banz and Miller (1978). Particular attention is paid to valuing so-called path-dependent securities whose contemporaneous cash flows depend on the historical path of interest rates as well as their current level. A detailed example is provided in which an adjustable-rate mortgage is valued under a variety of economic and security specific assumptions.     

Term Structure Movements and Pricing Interest Rate Contingent Claims

This paper derives an arbitrage-free interest rate movements model (AR model). This model takes the complete term structure as given and derives the subsequent stochastic movement of the term structure such that the movement is arbitrage free. We then show that the AR model can be used to price interest rate contingent claims relative to the observed complete term structure of interest rates. This paper also studies the behavior and the economics of the model. Our approach can be used to price a broad range of interest rate contingent claims, including bond options and callable bonds.     

The prepayment option on mortgage securities: A random coefficient approach

Using the Swamy (1970) model for pooled data and a Hildreth and Houck (1968) model for individual securities, this article investigates whether the parameters describing the prepayment behavior of the fixed-rate debt underlying mortgage-backed securities are better estimated as a stochastic behavior. Empirical results indicate that differences between securities are random. The Hildreth and Houck model yields additional information on randomness over time. The use of the aggregate data to estimate prepayment of individual securities, as opposed to use of the prepayment history of the individual security, may yield more reliable results.     

A comparison of models for pricing interest rate derivative securities

This paper looks at the different approaches and different models that have been developed to value interest rate-dependent securities, providing a survey of pricing procedures which are based on mathematical models of the term structure. It can be viewed as a reference for the different interest rate models with explicit representations, where they exist, for prices of derivative instruments and an an analysis of their respective advantages and disadvantages.