Walter N. Torous

A Simplified Jump Process for Common Stock Returns

The specification of a statistical distribution which accurately models the behavior of stock returns continues to be a salient issue in financial economics. With the introduction of arithmetic and geometric Brownian motion models, much attention has recently focused on a Poisson mixture of distributions as an appropriate specification of stock returns. For example, see [12], [3], [8], [10], [5], and [1]. Consistent with empirical evidence, these models yield leptokurtic security return distributions and, furthermore, the specification has much economic intuition. In particular, one may always decompose the total change in stock price into “normal†and “abnormal†components. The “normal†change may be due to variation in capitalization rates, a temporary imbalance between supply and demand, or the receipt of any other information which causes marginal price changes. This component is modelled as a lognormal diffusion process. The “abnormal†change is due to the receipt of any information which causes a more than marginal change in the price of the stock and is usually modeled as a Poisson process.

A Comparison of UK, US and German Insolvency Codes

The bankruptcy codes of the United States, the United Kingdom and Germany differ concerning who is permitted to control the debtor in bankruptcy and as to the ability of the debtor to arrange new financing while in bankruptcy. This study compares the efficiency of these three bankruptcy codes against a set of benchmarks.

The stochastic volatility of short-term interest rates: Some international evidence

This paper estimates a stochastic volatility model of short-term riskless interest rate dynamics. Estimated interest rate dynamics are broadly similar across a number of countries and reliable evidence of stochastic volatility is found throughout. In contrast to stock returns, interest rate volatility exhibits faster mean-reverting behavior and innovations in interest rate volatility are negligibly correlated with innovations in interest rates. The less persistent behavior of interest rate volatility reflects the fact that interest rate dynamics are impacted by transient economic shocks such as central bank announcements and other macroeconomic news. Copyright The American Finance Association 1999.

Mortgage Prepayment and Default Decisions: A Poisson Regression Approach

This paper uses an extensive and geographically dispersed sample of single-family fixed rate mortgages to assess the prepayment and default behavior of individual homeowners. We make use of Poisson regression to efficiently estimate the parameters of a proportional hazards model for prepayment and default decisions. Poisson regression for grouped survival data has several advantages over partial likelihood methods. First, when dealing with time-dependent covar-iates, it is considerably more efficient in terms of computations. Second, it is possible to estimate full-hazard models which include, for example, functions of time as well as multiple time scales (i.e., age of the loan and calendar time), in a much more straightforward manner than partial likelihood methods for un-grouped data. Third, Poisson regression can be used to estimate non-proportional hazards models such as additive excess risk specifications. Taken together, our data and estimation methodology allow us to obtain a better understanding of the economic factors underlying prepayment and default decisions. Copyright American Real Estate and Urban Economics Association.

The Maximum Likelihood Estimation of Security Price Volatility: Theory, Evidence, and Application to Option Pricing

the market requires efficient estimation of the Assuming security price dynamics are governed by a diffusion process and given the publicly most available form of data, this paper provides the maximum likelihood estimator of security price volatility. A Monte Carlo simulation compares the small-sample properties of this and other proposed security price volatility estimators. The resultant maximum likelihood estimator of the Black-Scholes call option price formulation is also derived. For small sample sizes a Monte Carlo simulation study facilitates comparison with other proposed estimation procedures. Also, the statistically most powerful confidence intervals for the BlackScholes call option price are constructed. * We would like to thank the participants of the Statistics Department Seminar and Finance Department Workshop at the University of Michigan for their helpful comments. We are especially grateful to Fred Hoppe, Adrian Tschoegl, and an anonymous referee for their insightful suggestions. Any remaining errors are our responsibility.

Unit roots and the estimation of interest rate dynamics

This paper investigates the time series estimation of Cox, Ingersoll, and Rosss square root, mean-reverting specification for interest rate dynamics. For a priori resonable mean reversion, the stochastic behavior of interest rates is sufficiently close to a non-stationary process with a unit root so that least squares, the generalized method of moments, as well as maximum likelihood estimation provide upward biased estimates of the models speed of adjustment coefficient. Corresponding bond yields, as a result, exhibit excessive mean reversion. In addition, estimates of the specifications long-term mean interest rate are seen to display erratic behavior when near a unit root. These conclusions are robust to assuming multiple state variable specifications, such as Brennan and Schwartzs two factor model of interest rate dynamics. We also document conditions under which this unit root problem can be alleviated when the cross-sectional restrictions of the Cox, Ingersoll, and Ross single factor term structure model are imposed.

Bond Price Dynamics and Options

This paper provides a closed-form, preference-free means of valuing a European call option written on a default-free pure discount bond. Investors may not agree upon a theory of the term structure, but they will necessarily agree on equilibrium option values. Further, these equilibrium option values may be obtained without recourse to numerical approximation.Default-free pure discount bond prices were posited to follow a non-standardized transformed Brownian bridge process. This specification implicitly incorporates the terminal constraint that the price of a default-free pure discount bond equal its face value at maturity.Contingent claim valuation necessarily involves consideration of terminal constraints on the value of financial securities. The Brownian bridge specification permits an appropriate means of incorporating a number of such constraints. Therefore, while this paper has considered only the application of the Brownian bridge process to the valuation of debt options, the introduction of this process may provide for many further financial applications.

Forecasting Real Estate Prices

This chapter reviews the evidence of predictability in U.S. residential and commercial real estate markets. First, we highlight the main methodologies used in the construction of real estate indices, their underlying assumptions and their impact on the stochastic properties of the resultant series. We then survey the key empirical findings in the academic literature, including short-run persistence and long-run reversals in the log changes of real estate prices. Next, we summarize the ability of local as well as aggregate variables to forecast real estate returns. We illustrate a number of these results by relying on six aggregate indexes of the prices of unsecuritized (residential and commercial) real estate and REITs. The effect of leverage and monetary policy is also discussed.

Investigating security-price performance in the presence of event-date uncertainty

Abstract This paper introduces an event-study method that incorporates the possibility of a random event date. Consistent with empirical evidence, we assume an event may affect not only the conditional mean of a securitys return, but also its conditional variance. We compare the statistical power and efficiency of our maximum-likelihood method with the standard application of traditional event-study methods to multiday security returns. Assuming a two-day event period, our empirical results provide evidence that the multiday approach is robust. We use our maximum-likelihood method to investigate the valuation effects of stock splits and stock dividends.

The Cross-Sectional Dispersion of Commercial Real Estate Returns and Rent Growth: Time Variation and Economic Fluctuations

We estimate the cross-sectional dispersions of returns and growth in rents for commercial real estate using data on U.S. metropolitan areas over the sample period 1986 to 2002. The cross-sectional dispersion of returns is a measure of the risk faced by commercial real estate investors. We document that, for apartments, offices, industrial and retail properties, the cross-sectional dispersions are time varying. Interestingly, their time-series fluctuations can be explained by macroeconomic variables such as the term and credit spreads, inflation and the short rate of interest. The cross-sectional dispersions also exhibit an asymmetrically larger response to negative economics shocks, which may be attributable to credit channel effects impacting the availability of external debt financing to commercial real estate investments. Finally, we find a statistically reliable positive relation between commercial real estate returns and their cross-sectional dispersion, suggesting that idiosyncratic fluctuations are priced in the commercial real estate market.