Long-term factorization in Heath–Jarrow–Morton models

The long-term factorization decomposes the stochastic discount factor (SDF) into discounting at the rate of return on the long bond and a martingale that defines a long-term forward measure. We establish sufficient conditions for existence of the long-term factorization in HJM models. A condition on the forward rate volatility ensures existence of the long bond volatility. This yields existence of the long bond and convergence of \(T\)-forward measures to the long forward measure. It contrasts with the familiar risk-neutral factorization that decomposes the SDF into discounting at the short rate and a martingale defining the risk-neutral measure.     

Stochastic evolution equations in Banach spaces and applications to the Heath–Jarrow–Morton–Musiela equations

The aim of this paper is threefold. Firstly, we study stochastic evolution equations (with the linear part of the drift being a generator of a \(C_{0}\)-semigroup) driven by an infinite-dimensional cylindrical Wiener process. In particular, we prove, under some sufficient conditions on the coefficients, the existence and uniqueness of solutions for these stochastic evolution equations in a class of Banach spaces satisfying the so-called \(H\)-condition. Moreover, we analyse the Markov property of the solutions.Secondly, we apply the abstract results obtained in the first part to prove the existence and uniqueness of solutions to the Heath–Jarrow–Morton–Musiela (HJMM) equations in weighted Lebesgue and Sobolev spaces.Finally, we study the ergodic properties of the solutions to the HJMM equations. In particular, we find a sufficient condition for the existence and uniqueness of invariant measures for the Markov semigroup associated to the HJMM equations (when the coefficients are time-independent) in the weighted Lebesgue spaces.Our paper is a modest contribution to the theory of financial models in which the short rate can be undefined.     

Estimating the Gerber–Shiu function by Fourier–Sinc series expansion

In this paper, we consider the nonparametric estimation of the Gerber–Shiu function in a compound Poisson risk model perturbed by diffusion. We present a more efficient estimator based on Fourier–Sinc series expansion. Our estimator is easily computed and has a faster convergence rate. Some simulation examples are provided to show that the estimator performs well when the sample size is finite.     

Consumption–investment optimization with Epstein–Zin utility in incomplete markets

In a market with stochastic investment opportunities, we study an optimal consumption–investment problem for an agent with recursive utility of Epstein–Zin type. Focusing on the empirically relevant specification where both risk aversion and elasticity of intertemporal substitution are in excess of one, we characterize optimal consumption and investment strategies via backward stochastic differential equations. The superdifferential of indirect utility is also obtained, meeting demands from applications in which Epstein–Zin utilities were used to resolve several asset pricing puzzles. The empirically relevant utility specification introduces difficulties to the optimization problem due to the fact that the Epstein–Zin aggregator is neither Lipschitz nor jointly concave in all its variables.     

Runs,panics and bubbles: Diamond–Dybvig and Morris–Shin reconsidered

The basic two-noncooperative-equilibrium-point model of Diamond and Dybvig is considered along with the work of Morris and Shin utilizing the possibility of outside noise to select a unique equilibrium point. Both of these approaches are essentially nondynamic. We add an explicit replicator dynamic from evolutionary game theory to provide for a sensitivity analysis that encompasses both models and contains the results of both depending on parameter settings.     

Mean–variance and mean–semivariance portfolio selection: a multivariate nonparametric approach

While univariate nonparametric estimation methods have been developed for estimating returns in mean-downside risk portfolio optimization, the problem of handling possible cross-correlations in a vector of asset returns has not been addressed in portfolio selection. We present a novel multivariate nonparametric portfolio optimization procedure using kernel-based estimators of the conditional mean and the conditional median. The method accounts for the covariance structure information from the full set of returns. We also provide two computational algorithms to implement the estimators. Via the analysis of 24 French stock market returns, we evaluate the in-sample and out-of-sample performance of both portfolio selection algorithms against optimal portfolios selected by classical and univariate nonparametric methods for three highly different time periods and different levels of expected return. By allowing for cross-correlations among returns, our results suggest that the proposed multivariate nonparametric method is a useful extension of standard univariate nonparametric portfolio selection approaches.     

Input–output-based measures of systemic importance

The analyses of intersectoral linkages of Leontief [The Structure of the American Economy: 1919–1929, 1941] and Hirschman [The Strategy of Economic Development, 1958] provide a natural way to study the transmission of risk among interconnected banks and to measure their systemic importance. In this paper, we show how elements from classic input–output analysis can be applied to banking and how to derive six indicators that capture different aspects of systemic importance, using a simple numerical example for illustration. We also discuss the relationship with other approaches, most notably network centrality measures, both formally and by means of a simulated network.     

Mean–variance convergence around the world

In this paper, we show (i) that the risk-return characteristics of our sample of 17 developed stock markets of the world have converged significantly toward each other during our study period 1974–2007, and (ii) that this international convergence in risk-return characteristics is driven mainly by the declining ‘country effect’, rather than the rising ‘industry effect’, suggesting that the convergence is associated with international market integration. Specifically, we first compute the risk-return distance among international stock markets based on the Euclidean distance and find that the distance thus computed has been decreasing significantly over time, implying a mean–variance convergence. In particular, the average risk-return distance has decreased by about 50% over our sample period. We also document that the risk-return characteristics of our sample of 14 emerging markets have been converging rapidly toward those of developed markets in recent years. This development notwithstanding, emerging markets still remain as a distinct asset class. Lastly, we show that the convergence in risk-return characteristics has exerted a negative impact on the efficiency of international investment during our sample period.     

Price–volume relations of DAX companies

This study provides empirical evidence of the joint dynamics between stock returns and trading volume using stock data of DAX companies. Contemporaneous as well as dynamic interactions are investigated for a period from January 1994 to December 2005 on a daily basis. Our results suggest that there is almost no relationship between stock return levels and trading volume in either direction. We find that trading volume is contemporaneously positively related to return volatility. In addition, we establish that lagged return volatility induces trading volume movements. Finally, we examine dependencies in the tails and find no significant support for the hypothesis of the independence of the maximal values of absolute returns and trading volume.

Predictability and the earnings–returns relation

This paper studies the effects of predictability on the earnings–returns relation for individual firms and for the aggregate. We demonstrate that prices better anticipate earnings growth at the aggregate level than at the firm level, which implies that random-walk models are inappropriate for gauging aggregate earnings expectations. Moreover, we show that the contemporaneous correlation of earnings growth and stock returns decreases with the ability to predict future earnings. Our results may therefore help explain the apparently conflicting recent evidence that the earnings–returns relation is negative at the aggregate level but positive at the firm level.     

Commutation functions under Gompertz–Makeham mortality

It is known, but perhaps not well-known, that when the mortality is assumed to be of Gompertz–Makeham-type, the expected remaining life-length and the commutation functions used for calculating the expected values of various types of life insurances can be expressed with an incomplete gamma function with a negative shape parameter. This is not of much use if ones software cannot calculate these values. The aim of this note is to show that one can express the commutation functions using only the exponential function, the (ordinary) gamma function and the gamma distribution function, which are all implemented in common statistical and spreadsheet software. This eliminates the need to evaluate the commutation functions and expected remaining life-length with numerical integration.     

Information asymmetry and investment–cash flow sensitivity

Models of capital market imperfections predict that information asymmetry decreases firm investment and increases the sensitivity of investment expenditures to fluctuations in internal funds. Previous empirical tests of the link between investment and financing decisions have relied on indirect measures of financial constraint due to market frictions. In contrast, we use more direct measures derived from the market microstructure literature. Consistent with the theoretical predictions, our analysis shows that scaled investment expenditures are on average lower and the investment–cash flow sensitivity is greater when the probability of informed trading is high. Our results are robust to alternative measures of informed trading and liquidity, but they are not pervasive in our sample.     

Statistical arbitrage in the Black–Scholes framework

In this study, we prove the existence of statistical arbitrage opportunities in the Black–Scholes framework by considering trading strategies that consist of borrowing at the risk-free rate and taking a long position in the stock until it hits a deterministic barrier level. We derive analytical formulas for the expected value, variance and probability of loss for the discounted cumulative trading profits. The statistical arbitrage condition is derived in the Black–Scholes framework, which imposes a constraint on the Sharpe ratio of the stock. Furthermore, we verify our theoretical results via extensive Monte Carlo simulations.