Specifying a consistent joint maximum-likelihood (JMLE) approach to testing bond models

In this paper we extend the results derived in our earlier work to develop a methodology to employ the maximum-likelihood estimation technique for the pricing of interest rate instruments. In order to price bonds and their derivative assets, researchers must identify a preference parameter in addition to the dynamics for the interest rate process. There are two approaches to obtaining estimators for both preference and dynamics parameters: (1) a two-stage approach and (2) a single-stage joint maximum-likelihood (JMLE) approach. The first approach, while tractable, suffers from serious drawbacks, primarily those relating to the use of the estimates from the first stage in estimating parameters in the second stage. In this paper, we develop the theory necessary for joint maximum-likelihood (JMLE) over the set of bond prices and the interest rate. We operationalize the theory by assuming that the error processes for all coupon bonds are mutually independent and uniformly distributed with a mean of zero. This specification is at least partially justifiable by the observation that since market prices are quoted in 1/32 of a dollar, theoretical prices must always be rounded either up or down. JML estimators can be obtained from the joint log-likelihood function by the methods of sequential quadratic programming

MLE is alive and well in the financial markets

In this paper we specify the basic set of economic criteria that any diffusion-driven interest rate or FX rate process must satisfy. We also develop the methodology that is implementable to test the validity of a proposed process insofar as it satisfies the basic criteria as well as the actual estimation of the parameters of an acceptable candidate process. In this paper we focus on processes such as the overnight repo rate process or the FX rate process, each of which is directly observable. We develop what we call the marginal maximum-likelihood estimation (MMLE) technique to distinguish it from the joint maximum-likelihood estimation (JMLE) technique, which we present in a separate paper. We also present some preliminary empirical results for both the interest rate process and the FX rate process

Price reactions to public announcements

We employ a parametric rational expectations equilibrium model to study the impact of public information releases on private information acquisition and asset prices in a large economy. We demonstrate that investors treat public information as a substitute for privately acquired information. Their attempts to substitute public for private information can amplify or even reverse the effect of public information releases on price volatility. The direction of the resulting change in price volatility is dependent on the level of public information regarding asset payoffs, the variance of asset payoffs, and the extent of supply shocks, implying that firms may differ in their optimal information release policies

Applying economic restrictions to foreign exchange rate dynamics: spot rates, futures, and options

Extant models of exchange rate behavior have typically relied on statistical rather than economic considerations. The approach has been to employ a variant of the generalized central limit theorem to develop tests for the models proposed. ; We propose a minimal set of simple economic restrictions symmetry, invariance, and non-negativity that must be satisfied by an exchange rate process. By symmetry, we mean that both the direct and indirect exchange rate processes must belong to the same class of distributions. By invariance, we mean that the distribution for an exchange rate must be invariant to changes in the currency unit. By non-negativity, we mean that the exchange rate process must preclude negative values. We identify various alternative specifications for exchange rate processes and show that some of them do not possess some or all of the above properties. Finally, we propose a new exchange rate process -- the mean-reverting logarithmic process (MRL) -- and develop valuation equations for several exchange rate instruments, from forward and futures contracts to straight options on the spot rates to options on the futures contracts

Rational expectations equilibrium in an economy with segmented capital asset markets

We develop a model of noisy rational expectations equilibrium in segmented markets. The noise emerges endogenously through intermarket effects rather than through exogenous supply noise from liquidity or naive trading as in standard noisy rational expectations equilibrium of the Hellwig type. Existence of and persistence of segmentation in equilibrium is established. A metric to determine welfare effects of the degree of segmentation is also derived. This metric is structurally different from the metric derived in the standard models and includes the latter as a special case. Empirical evidence from and observed characteristics of "real world" economies that support the economic intuition underlying the model are described in some detail

An intertemporal model of consumption and portfolio allocation

We develop an infinite time horizon, continuous time model of portfolio choice and consumption allocation for an investor seeking to maximize the expected utility of his life-time consumption. In this model, the investor is endowed with capital that can be invested in long-lived capital assets and has, in addition, a stochastic stream of cash flows that could be interpreted as either a wage income stream or a stochastic endowment flow. We obtain a complete and original solution to the consumption-portfolio choice problem for the negative exponential and quadratic utility functions and special case solutions for the general power and log utility functions. The results obtained in this paper have significant implications for the theory of asset prices, the theory of mutual funds, optimal portfolio strategies of investors, and so forth. The results of the model can also be easily extended to one with a finite time horizon

Off-farm income and risk reduction in agriculture: when does it matter?

Investment behavior is analyzed using a dynamic portfolio model including off-farm income. The correlation structure of off-farm income and asset returns and the ratio of off-farm income to wealth is shown to affect portfolio choice. Empirical analysis indicates that off-farm income tends to increase farm assets

Off-farm income and risk reduction in agriculture: when does it matter?

Investment behavior is analyzed using a dynamic portfolio model including off-farm income. The correlation structure of off-farm income and asset returns and the ratio of off-farm income to wealth is shown to affect portfolio choice. Empirical analysis indicates that off-farm income tends to increase farm assets.Agriculture ; Farm income ; Wages

Estimation of risk-neutral and statistical densities by Hermite polynomial approximation: with an application to Eurodollar futures options

This paper expands and tests the approach of Madan and Milne (1994) for pricing contingent claims as elements of a separable Hilbert space. We specialize the Hilbert space basis to the family of Hermite polynomials and use the model to price options on Eurodollar futures. Restrictions on the prices of Hermite polynomial risk for contingent claims with different times to maturity are derived. These restrictions are rejected by our empirical tests of a four-parameter model. The unrestricted results indicate skewness and excess kurtosis in the implied risk-neutral density. These characteristics of the density are also mirrored in the statistical density estimated from a time series on LIBOR. The out-of-sample performance of the four-parameter model is consistently better than that of a two-parameter version of the model