Discussions on the spurious hyperbolic memory in the conditional variance and a new model

This paper studies the spurious hyperbolic memory in the conditional variance caused by the Markov Regime-Switching GARCH (MRS-GARCH) process. We firstly propose an illustrative cause of this spuriousness and provide simulation evidence. An MRS Hyperbolic GARCH (MRS-HGARCH) model is then developed to successfully address it. Related statistical properties including the stationarity conditions and asymptotic behaviours of the maximum likelihood estimators of the MRS-HGARCH process are also investigated. An empirical study of the S&P 500 and TOPIX indexes returns is then conducted which demonstrates that our MRS-HGARCH model can provide a more reliable estimator of the hyperbolic-memory parameter and outperform both the HGARCH and MRS-GARCH models.     

Cramér–Von Mises distance estimation for some positive infinitely divisible parametric families with actuarial applications

Cramér–Von Mises (CVM) inference techniques are developed for some positive flexible infinitely divisible parametric families generalizing the compound Poisson family. These larger families appear to be useful for parametric inference for positive data. The methods are based on inverting the characteristic functions. They are numerically implementable whenever the characteristic function has a closed form. In general, likelihood methods based on density functions are more difficult to implement. CVM methods also lead to model testing, with test statistics asymptotically following a chi-square distribution. The methods are for continuous models, but they can also handle models with a discontinuity point at the origin such as the case of compound Poisson models. Simulation studies seem to suggest that CVM estimators are more efficient than moment estimators for the common range of the compound Poisson gamma family. Actuarial applications include estimation of the stop loss premium, and estimation of the present value of cash flows when interest rates are assumed to be driven by a corresponding Lévy process.     

Cross‐sectional Restrictions on the Spot and Forward Term Structures of Interest Rates and Panel Unit Root Tests

In this paper we examine the stationarity of all the rates comprising the USD, GBP, DM and JPY spot and forward term structures. Instead of focussing on short maturity interest rates, as most other papers do, we perform a detailed analysis of the whole range of spot and forward interest rates of the 4 main currencies. We investigate the issue of stationarity within the framework of an equilibrium interest rate model such as Vasicek (1977), that defines the cross-sectional and time series properties that interest rates of various maturities must satisfy. We show that within a one-factor interest rate model, such as Vasicek, all interest rates are restricted to exhibit the same mean reverting behaviour. This restriction allows us to apply more powerful panel unit root tests. This methodology increases considerably the number of observations available and as a result the power of the unit root tests. The higher power of these tests allows us to demonstrate that there does exist mean reversion on the spot and forward US interest rates and the forward DM and GBP interest rates.     

Simulated likelihood estimation of diffusions with an application to exchange rate dynamics in incomplete markets

We present an econometric method for estimating the parameters of a diffusion model from discretely sampled data. The estimator is transparent, adaptive, and inherits the asymptotic properties of the generally unattainable maximum likelihood estimator. We use this method to estimate a new continuous-time model of the joint dynamics of interest rates in two countries and the exchange rate between the two currencies. The model allows financial markets to be incomplete and specifies the degree of incompleteness as a stochastic process. Our empirical results offer several new insights into the dynamics of exchange rates.     

Nonparametric estimation of scalar diffusion models of interest rates using asymmetric kernels

This paper proposes an asymmetric kernel-based method for nonparametric estimation of scalar diffusion models of spot interest rates. We derive the asymptotic theory for the asymmetric kernel estimators of the drift and diffusion functions for general and positive recurrent processes and illustrate the advantages of the Gamma kernel for bias correction and efficiency gains. The finite-sample properties and the practical relevance of the proposed nonparametric estimators for bond and option pricing are evaluated using actual and simulated data for U.S. interest rates.     

Analysis of Consumers’ Perceptions of Buying Conditions for Houses

This paper examines the determinants of consumers’ buying attitudes for houses from January 1984 through June 2005. Data on buying attitudes are from responses to the Surveys of Consumer Attitudes conducted by the Survey Research Center, University of Michigan. The determinants considered include current and expected interest rates, wealth, expected real disposable income, expected change in financial status and house prices. The empirical estimates show that a long-run relationship exists between buying attitudes for houses and each of the above variables. Each of these determinants also Granger cause buying perceptions. Generalized impulse responses show that shocks to each of the above variables have a predictable and permanent impact on buying attitudes. Furthermore, generalized variance decompositions suggest that both current and expected interest rates explain a large proportion of the variation in consumers’ perceptions towards buying houses. Since consumers’ attitudes towards buying houses are likely to be translated into actual purchases, this study shows that in order of importance, interest rates—both current and future—have the maximum impact on decisions to purchase houses followed by expectations of real disposable income.

Likelihood-based specification analysis of continuous-time models of the short-term interest rate

An extensive collection of continuous-time models of the short-term interest rate is evaluated over data sets that have appeared previously in the literature. The analysis, which uses the simulated maximum likelihood procedure proposed by Durham and Gallant (2002), provides new insights regarding several previously unresolved questions. For single factor models, I find that the volatility, not the drift, is the critical component in model specification. Allowing for additional flexibility beyond a constant term in the drift provides negligible benefit. While constant drift would appear to imply that the short rate is nonstationary, in fact, stationarity is volatility-induced. The simple constant elasticity of volatility model fits weekly observations of the three-month Treasury bill rate remarkably well but is easily rejected when compared with more flexible volatility specifications over daily data. The methodology of Durham and Gallant can also be used to estimate stochastic volatility models. While adding the latent volatility component provides a large improvement in the likelihood for the physical process, it does little to improve bond-pricing performance.     

A Generalization of the Formulas for Options on the Maximum or the Minimum of Several Assets

Abstract

This paper generalizes the option on the maximum or the minimum of two assets (several assets) within a stochastic interest rate framework. A Gaussian model is used to describe the interest rates. Closed-form solutions for the market values are presented. The use of the options is illustrated with numerical examples.     

Marginal consistent dependence modelling using weak subordination for Brownian motions

We present an approach for modelling dependencies in exponential Lévy market models with arbitrary margins originated from time changed Brownian motions. Using weak subordination of Buchmann et al. [Bernoulli, 2017], we face a new layer of dependencies, superior to traditional approaches based on pathwise subordination, since weakly subordinated processes are not required to have independent components considering multivariate stochastic time changes. We apply a subordinator being able to incorporate any joint or idiosyncratic information arrivals. We emphasize multivariate variance gamma and normal inverse Gaussian processes and state explicit formulae for the Lévy characteristics. Using maximum likelihood, we estimate multivariate variance gamma models on various market data and show that these models are highly preferable to traditional approaches. Consistent values of basket-options under given marginal pricing models are achieved using the Esscher transform, generating a non-flat implied correlation surface.     

Bayesian estimation of financial models

This paper outlines a general methodology for estimating the parameters of financial models commonly employed in the literature. A numerical Bayesian technique is utilised to obtain the posterior density of model parameters and functions thereof. Unlike maximum likelihood estimation, where inference is only justified in large samples, the Bayesian densities are exact for any sample size. A series of simulation studies are conducted to compare the properties of point estimates, the distribution of option and bond prices, and the power of specification tests under maximum likelihood and Bayesian methods. Results suggest that maximum–likelihood–based asymptotic distributions have poor finite–sampleproperties.     

A discrete and a continuous-time model based on a technical trading rule

In this article we propose a model in discrete and continuoustime that incorporates explicitly a technical trading rule inthe specification of the volatility. The proposed discrete-timemodel is an alternative to GARCH-type processes. We derive conditionsfor the covariance and strict stationarity of the discrete-timeprocess and we study the estimation and inference problems.We also analyze the conditions under which the discrete-timeprocess converges in distribution to a diffusion process. Toillustrate the proposed model and compare it with the GARCHspecification, we analyze the daily closing stock prices oftwo major U.S. companies (Microsoft and Oracle), two stock indices(DAX and NASDAQ) and two U.S. Dollar exchange rates (Euro andSterling)     

Factors driving aggregate mortality rates in postwar Germany

Using German data over the period 1956–2006, this study provides a comprehensive empirical analysis of factors driving aggregate mortality rates over time. It differs from previous contributions in this field by simultaneously considering an extensive set of macroeconomic, socioeconomic, and ecological factors as explanatory variables. Our regression analysis shows that sex- and age-specific mortality rates vary substantially in their response to external factors. Strongest associations are found with changes in real GDP, flu epidemics, and the two lifestyle variables—alcohol and cigarette consumption—in both univariate and multivariate setups. Further analysis indicates that these effects are primarily contemporary, whereas other indicators, such as weather conditions, exert lagged effects. We derive optimal multivariate models for every age group that provide a good fit to the observed variation in annual mortality rates, and thereby confirm the relevance of the identified factors.     

Reduced-form Models with Regime Switching: An Empirical Analysis for Corporate Bonds

Empirical evidence shows that there is a close link between regime shifts and business cycle fluctuations. A standard term structure of interest rates, such as the Cox et al. (1985 Econometrica, 53, 385–407; CIR) model, is sharply rejected in the Treasury bond data. Only Markov regime-switching models on the entire yield curve of the Treasury bond data can account for the observed behavior of the yield curve. In this paper, we examine the impact of regime shifts on AAA-rated and BBB-rated corporate bonds through the use of a reduced-form model. The model is estimated by the Efficient Method of Moments (EMM). Our empirical results suggest that regime-switching risk has significant implications for corporate bond prices and hence has a material impact on the entire corporate bond yield curve, providing evidence for the approach of rating through the cycle employed by rating agencies.     

Fractionally Integrated Models With ARCH Errors: With an Application to the Swiss 1-Month Euromarket Interest Rate

We introduce ARFIMA-ARCH models, which simultaneously incorporate fractional differencing and conditional heteroskedasticity. We develop the likelihood function and we use it to construct the bias-corrected maximum (modified profile) likelihood estimator. Finite-sample properties of the estimation procedure are explored by Monte Carlo simulation. Backus and Zin (1993) have motivated the existence of fractional integration in interest rates by the persistence of the short rate and the variability of the long end of the yield curve. An empirical investigation of a daily one-month Swiss Euromarket interest rate finds a difference parameter of 0.72. This indicates non-stationary behavior. In contrast to first-order integrated models, the long-run cumulative response of shocks to the series is zero.     

Repeat Sales Index for Thin Markets

The repeat sales model is commonly used to construct reliable house price indices in absence of individual characteristics of the real estate. Several adaptations of the original model by Bailey et al. (J Am Stat Assoc 58:933–942, 1963) are proposed in literature. They all have in common using a dummy variable approach for measuring price indices. In order to reduce the impact of transaction price noise on the estimates of price indices, Goetzmann (J Real Estate Finance Econ 5:5–53, 1992) used a random walk with drift process for the log price levels instead of the dummy variable approach. The model that is proposed in this article can be interpreted as a generalization of the Goetzmann methodology. We replace the random walk with drift model by a structural time series model, in particular by a local linear trend model in which both the level and the drift parameter can vary over time. An additional variable—the reciprocal of the time between sales—is included in the repeat sales model to deal with the effect of the time between sales on the estimated returns. This approach is robust can be applied in thin markets where relatively few selling prices are available. Contrary to the dummy variable approach, the structural time series model enables prediction of the price level based on preceding and subsequent information, implying that even for particular time periods where no observations are available an estimate of the price level can be provided. Conditional on the variance parameters, an estimate of the price level can be obtained by applying regression in the general linear model with a prior for the price level, generated by the local linear trend model. The variance parameters can be estimated by maximum likelihood. The model is applied to several subsets of selling prices in the Netherlands. Results are compared to standard repeat sales models, including the Goetzmann model.     

Auction failures and the market for auction rate securities

The market for auction rate securities (ARS) made headlines during the second week of February 2008 when auctions at which the bonds’ interest rates reset experienced a wave of “failures.” Contrary to headlines that attribute the failures to a “frozen” market or investors’ “irrationality,” we find that (1) even at their height, less than 50% of ARS experienced auction failures, (2) the likelihood of auction failure was directly related to the level of the bonds’ “maximum auction rates,” (3) the implied market clearing yields of bonds with failed auctions were significantly above their maximum auction rates, and (4) ARS yields were generally higher than yields of various cash equivalent investment alternatives. We infer that investors priced the possibility of auctions failures into ARS yields and rationally declined to bid for bonds for which required market yields exceeded their maximum auction rates.     

Selecting copulas for risk management

Copulas offer financial risk managers a powerful tool to model the dependence between the different elements of a portfolio and are preferable to the traditional, correlation-based approach. In this paper, we show the importance of selecting an accurate copula for risk management. We extend standard goodness-of-fit tests to copulas. Contrary to existing, indirect tests, these tests can be applied to any copula of any dimension and are based on a direct comparison of a given copula with observed data. For a portfolio consisting of stocks, bonds and real estate, these tests provide clear evidence in favor of the Student’s t copula, and reject both the correlation-based Gaussian copula and the extreme value-based Gumbel copula. In comparison with the Student’s t copula, we find that the Gaussian copula underestimates the probability of joint extreme downward movements, while the Gumbel copula overestimates this risk. Similarly we establish that the Gaussian copula is too optimistic on diversification benefits, while the Gumbel copula is too pessimistic. Moreover, these differences are significant.     

Nominal interest rates and stationarity

This paper investigates the (break) stationarity null hypothesis using data for 25 interest rates with different maturities and risk characteristics in Canada and the US. In contrast to a large part of the literature, this paper reports strong empirical evidence in favour of the null hypothesis of stationarity for the interest rate series.     

A study of diffusion processes for foreign exchange rates

The nature of the stochastic process generating the time path of foreign exchange rates plays an important role in dynamic theories of international financial economics. An important consideration in this stochastic process is the relationship between currency return variances and exchange rate levels. Using five years of daily data separated into quarterly intervals, this study demonstrates that currency return variances depend on exchange rate levels and the dependency is unstable intertemporally. Thus, these empirical results contradict the assumption of stable log-normal distribution and the more general assumption of constant elasticities of variances. For elasticity coefficients ordinary least squares estimates are compared to maximum likelihood estimates; the maximum likelihood estimator clearly is superior. Implications of these results for models of foreign exchange rates are discussed.     

Modeling International Long-Term Interest Rates

This study investigates the relationship among interest rates on the long-term government bonds of five industrialized countries. Both standard and new unit root tests are applied, all of which confirm the presence of exactly one unit root. New cointegration tests are also applied to these data. In contrast to previous research on short-term bonds, stock prices, and exchange rates, these results find little evidence of cointegration among the five long-term interest rate series. Thus, when modeling or forecasting these central government long-term bond yields, one may assume separate sets of fundamentals and difference the data to achieve stationarity. An error correction model may not be appropriate.