International Journal of Theoretical and Applied Finance

An arbitrage-free CEV economy driven by Brownian motion in independent, continuous random time is introduced. European options are priced by the no-arbitrage principle as conditional averages of their classical CEV values over the CEV-modified random time to maturity. A novel representation of the classical CEV price is used to investigate the asymptotics of the average implied volatility. It is shown that the average implied volatility of the at-the-money call option is lower and of deep out-of-the-money call options, under appropriate sufficient conditions, greater than the implied CEV volatilities. Unlike in the classical CEV model, the shape of the out-of-the-money tail can be both downward and upward sloping depending on the tails of random time. The model is implemented in limit lognormal time. Its multiscaling law is shown to imply a term structure of implied volatility that is qualitatively more sensitive to changes in the time to maturity than is the classical CEV model.

Since the equity premium as well as the risk-free rate puzzle question the concepts central to financial and economic modeling, we apply behavioral decision theory to asset pricing in view of solving these puzzles. US stock market data for the period 1960–2003 and German stock market data for the period 1977–2003 show that emotional investors who act in accordance to Bell's [6] disappointment theory — a special case of prospect theory — and additionally administer mental accounts demand a high equity premium. Furthermore, these investors reason a low risk-free rate. However, Barberis et al. [5] already showed that limited rational investors demand a high equity premium. But as opposed to them, our approach additionally supports dividend smoothing.

We present a general framework for considering investment in defaultable securities which — as special cases — includes both the firm value and the intensity based approach to credit risky bonds. In this framework, we construct a dynamically evolving portfolio of high-yield bonds where whenever a bond defaults it is replaced by another high yield bond. The properties of this portfolio and in particular the evolution of its face value are investigated. The modeling potential of our framework is demonstrated via examples of bond portfolios admitting extreme properties such as an unbounded face value process.

We formulate the portfolio choice problem as a robust control problem under uncertainty or ambiguity aversion. By considering a stochastic investment opportunity set, we derive optimal robust portfolio rules in the cases of one and two risky assets. With two risky assets and ambiguity structure determined by economy-wide factors, we show that the robust portfolio rule could lead to an increase in the total holdings of risky assets as compared to the holdings under the Merton rule, which is the standard risk aversion case. This result goes against the general belief that uncertainty aversion and robust control methods lead to conservative behavior. We also show that the investor is more likely to increase the holdings of the asset for which there is no ambiguity, and reduce the holdings of the asset for which there is ambiguity, a result that might provide an explanation for the home bias puzzle.

The model parameters in optimal asset allocation problems are often assumed to be deterministic. This is not a realistic assumption since most parameters are not known exactly and therefore have to be estimated. We consider investment opportunities which are modeled as local geometric Brownian motions whose drift terms may be stochastic and not necessarily measurable. The drift terms of the risky assets are assumed to be affine functions of some arbitrary factors. These factors themselves may be stochastic processes. They are modeled to have a mean-reverting behavior. We consider two types of factors, namely observable and unobservable ones. The closed-form solution of the general problem is derived. The investor is assumed to have either constant relative risk aversion (CRRA) or constant absolute risk aversion (CARA). The optimal asset allocation under partial information is derived by transforming the problem into a full-information problem, where the solution is well known. The analytical result is empirically tested in a real-world application. In our case, we consider the optimal management of a balanced fund mandate. The unobservable risk factors are estimated with a Kalman filter. We compare the results of the partial-information strategy with the corresponding full-information strategy. We find that using a partial-information approach yields much better results in terms of Sharpe ratios than the full-information approach.

We compare in a backtesting study the performance of univariate models for Value-at-Risk (VaR) and expected shortfall based on stable laws and on extreme value theory (EVT). Analyzing these different approaches, we test whether the sum–stability assumption or the max–stability assumption, that respectively imply α–stable laws and Generalized Extreme Value (GEV) distributions, is more suitable for risk management based on VaR and expected shortfall. Our numerical results indicate that α–stable models tend to outperform pure EVT-based methods (especially those obtained by the so-called block maxima method) in the estimation of Value-at-Risk, while a peaks-over-threshold method turns out to be preferable for the estimation of expected shortfall. We also find empirical evidence that some simple semiparametric EVT-based methods perform well in the estimation of VaR.

Market efficiency is an area of enormous interest in financial literature. Numerous researchers conducted empirical studies in testing weak-form market efficiency in several stock markets and employed various techniques but the empirical evidence is controversial. Triangulation econometric approach is employed to assess the predictability of daily return series of Botswana Stock Exchange (BSE) and to test the null hypothesis of random walk model. The empirical results reject the null hypothesis of random walk model for the daily return series of BSE for the period of 1989–2005 and evidenced serial autocorrelation of return series, which clearly indicate predictability and volatility of security prices of Botswana market. However, the empirical evidence of both non-parametric (Kolmogrov–Smirnov: normality test and run test) and parametric test (Auto-correlation test, Auto-regressive model, ARIMA model) reject the hypothesis of random walk model and indeed violate the notion of weak-form market efficiency.

The purpose of this paper is to show that an algorithm recently proposed by authors can in fact solve a maximal predictability portfolio (MPP) optimization problem, which is a hard nonconvex fractional programming optimization. Also, we will compare MPP with standard mean-variance portfolio (MVP) and show that MPP outperforms MVP and index. We believe that this paper is of interest to researchers and practitioners in the field of portfolio optimization.