Do local analysts have an informational advantage in forecasting stock returns? Evidence from the German DAX30

Utilizing data from the German DAX30 stock index, we investigate whether local analysts have an informational advantage in forecasting stock returns. We analyze whether banks’ buy and sell recommendations improve on the out-of-sample predictability of daily stock returns and the market-timing ability of investors who base their decisions on such recommendations. We find that, indeed, in a few cases German banks do have better stock-forecasting ability for daily stock returns than do foreign banks. However, the value added of bank recommendations is generally small and sensitive to the model-selection criterion used by an investor in setting up a forecasting model for stock returns.     

Optimal investment under multi-factor stochastic volatility

We consider a model for multivariate intertemporal portfolio choice in complete and incomplete markets with a multi-factor stochastic covariance matrix of asset returns. The optimal investment strategies are derived in closed form. We estimate the model parameters and illustrate the optimal investment based on two stock indices: S&P500 and DAX. It is also shown that the model satisfies several stylized facts well known in the literature. We analyse the welfare losses due to suboptimal investment strategies and we find that investors who invest myopically, ignore derivative assets, model volatility by one factor and ignore stochastic covariance between asset returns can incur significant welfare losses.     

Mean-reversion properties of implied volatilities

In this paper, we present a new stylized fact for options whose underlying asset is a stock index. Extracting implied volatility time series from call and put options on the Deutscher Aktien index (DAX) and financial times stock exchange index (FTSE), we show that the persistence of these volatilities depends on the moneyness of the options used for its computation. Using a functional autoregressive model, we show that this effect is statistically significant. Surprisingly, we show that the diffusion-based stochastic volatility models are not consistent with this stylized fact. Finally, we argue that adding jumps to a diffusion-based volatility model help recovering this volatility pattern. This suggests that the persistence of implied volatilities can be related to the tails of the underlying volatility process: this corroborates the intuition that the liquidity of the options across moneynesses introduces an additional risk factor to the one usually considered.     

A nesting framework for Markov-switching GARCH modelling with an application to the German stock market

In this paper, we establish a generalized two-regime Markov-switching GARCH model which enables us to specify complex (symmetric and asymmetric) GARCH equations that may differ considerably in their functional forms across the two Markov regimes. We show how previously proposed collapsing procedures for the Markov-switching GARCH model can be extended to estimate our general specification by means of classical maximum-likelihood methods. We estimate several variants of the generalized Markov-switching GARCH model using daily excess returns of the German stock market index DAX sampled during the last decade. Our empirical study has two major findings. First, our generalized model outperforms all nested specifications in terms of (a) statistical fit (when model selection is based on likelihood ratio tests) and (b) out-of-sample volatility forecasting performance. Second, we find significant Markov-switching structures in German stock market data, with substantially differing volatility equations across the regimes.     

HARA utility maximization in a Markov-switching bond–stock market

We present a flexible multidimensional bond–stock model incorporating regime switching, a stochastic short rate and further stochastic factors, such as stochastic asset covariance. In this framework we consider an investor whose risk preferences are characterized by the hyperbolic absolute risk-aversion utility function and solve the problem of optimizing the expected utility from her terminal wealth. For the optimal portfolio we obtain a constant-proportion portfolio insurance-type strategy with a Markov-switching stochastic multiplier and prove that it assures a lower bound on the terminal wealth. Explicit and easy-to-use verification theorems are proven. Furthermore, we apply the results to a specific model. We estimate the model parameters and test the performance of the derived optimal strategy using real data. The influence of the investor’s risk preferences and the model parameters on the portfolio is studied in detail. A comparison to the results with the power utility function is also provided.     

基于贝叶斯MSSV-ST金融波动模型的股市特征及机制转移性研究

针对有偏厚尾金融随机波动模型难以刻画参数的动态时变性及结构突变的问题,设置偏态参数服从 Markov 转换过程,采用贝叶斯方法,构建带机制转移的有偏厚尾金融随机波动模型,考量股市不同波动状态间的机制转移性,捕捉股市间多重波动特性。通过设置先验分布,实现模型的贝叶斯推断,设计相应的马尔科夫链蒙特卡洛算法进行估计,并利用上证指数进行实证。结果表明：模型不仅刻画了股市的尖峰厚尾、杠杆效应等特性,发现收益率条件分布的偏度参数具有动态时变性,股市波动呈现出显著的机制转移特性,而且证实了若模型考虑波动的不同阶段性状态后,将降低持续性参数向上偏倚幅度的结论。     

Estimation and pricing under long-memory stochastic volatility

We treat the problem of option pricing under a stochastic volatility model that exhibits long-range dependence. We model the price process as a Geometric Brownian Motion with volatility evolving as a fractional Ornstein–Uhlenbeck process. We assume that the model has long-memory, thus the memory parameter H in the volatility is greater than 0.5. Although the price process evolves in continuous time, the reality is that observations can only be collected in discrete time. Using historical stock price information we adapt an interacting particle stochastic filtering algorithm to estimate the stochastic volatility empirical distribution. In order to deal with the pricing problem we construct a multinomial recombining tree using sampled values of the volatility from the stochastic volatility empirical measure. Moreover, we describe how to estimate the parameters of our model, including the long-memory parameter of the fractional Brownian motion that drives the volatility process using an implied method. Finally, we compute option prices on the S&P 500 index and we compare our estimated prices with the market option prices.     

A new weighting-scheme for equity indexes

This paper proposes a novel methodology for computing a cross capitalization-weighted index, coined CCWI, that characterizes the most influential stocks that drive the index. The methodology, based on the factor analysis approach combined with the Equi-correlation model of Engle and Kelly (2012), encapsulates all the main information to replicate any given large equity stock index. We build a proxy that tracks accurately the S&P 500 while reducing the cost of duplication for large equity indexes with the methodology combining the PCA approach and the DECO model. We provide an application to the S&P 500 by constructing an aggregate stock index composed of the most influential stocks. The analysis reveals that the CCWI is useful for asset and risk management. Robustness checks expand the equity index universe to MIB, TSX, CAC, DAX, FTSE, NIKKEI, HSI and DJIA, both during full- and sub-periods.     

Zum fairen Wert der Aktienanlagen eines Lebensversicherungsunternehmens aus ökonomisch-statistischer Perspektive

The present contribution deals with the problem of an adequate determination of the “fair value” of the stock portfolio of a life insurance company taking an economical and statistical point of view. The starting point consists of three standard models from mathematical finance for the development of stock prices, the martingale model, the random walk model and the AR(l)-process, the latter as a basic model capturing mean reversion effects. The best (with respect to mean square error) forecast of the future value of the process given the information about its history then is a natural and model-based concept of a “fair value”. The question remaining now is which of the alternative models gives the best representation of the data. First of all it is explained, that the martingale hypothesis is valid neither from a theoretical from an empirical point of view. However, only in the case of a martingale the market value is the best forecast, i.e. only in this case the market value would correspond with the fair value in an economical-statistical sense. This implies that the common understanding in accounting practice that the market value is a natural candidate for the fair value is not justified in theoretical terms. With respect to the question “random walk or mean reversion?” we perform a statistical-econometrical analysis of a thirty year time series of the monthly price earnings ratios (PER) of the German stock index DAX. As a result, the AR(l)-process reveals to be a better statistical representative of the time series as the random walk. This implies, that the long term equilibrium value of the AR(l)-process is the best forecast of the fair value of the DAX-PER. Given that DAX-PER then — based on different assumptions about the earnings growth rate and the time horizon — corresponding forecasts are calculated for the DAX itself. Finally it is explained that because of the pronounced long term character of life insurance business this model based conception of a long-term fair value is ideally suited for an application to life insurance companies.     

A dynamic equilibrium model for U-shaped pricing kernels

This paper proposes a dynamic equilibrium model that can provide a unified explanation for the stylized facts observed in stock index markets such as the fat tails of the risk-neutral return distribution relative to the physical distribution, negative expected returns on deep OTM call options and negative realized variance risk premiums. In particular, we focus on the U-shaped pricing kernel against the stock index return, which is closely related to the negative call returns. We assume that the stock index return follows a time-changed Lévy process and that a representative investor has power utility over the aggregate consumption that forms a linear regression of the stock index return and its stochastic activity rate. This model offers a macroeconomic interpretation of the stylized facts from the perspective of the sensitivity of the activity rate and stock index return on aggregate consumption as well as the investor’s risk aversion.     

A semiparametric factor model for implied volatility surface dynamics

We propose a semiparametric factor model, which approximatesthe implied volatility surface (IVS) in a finite dimensionalfunction space. Unlike standard principal component approachestypically used to reduce complexity, our approach is tailoredto the degenerated design of IVS data. In particular, we onlyfit in the local neighborhood of the design points by exploitingthe expiry effect present in option data. Using DAX index optiondata, we estimate the nonparametric components and a low-dimensionaltime series of latent factors. The modeling approach is completedby studying vector autoregressive models fitted to the latentfactors.     

Stock market prediction using evolutionary support vector machines: an application to the ASE20 index

The main motivation for this paper is to introduce a novel hybrid method for the prediction of the directional movement of financial assets with an application to the ASE20 Greek stock index. Specifically, we use an alternative computational methodology named evolutionary support vector machine (ESVM) stock predictor for modeling and trading the ASE20 Greek stock index extending the universe of the examined inputs to include autoregressive inputs and moving averages of the ASE20 index and other four financial indices. The proposed hybrid method consists of a combination of genetic algorithms with support vector machines modified to uncover effective short-term trading models and overcome the limitations of existing methods. For comparison purposes, the trading performance of the ESVM stock predictor is benchmarked with four traditional strategies (a naïve strategy, a buy and hold strategy, a moving average convergence/divergence and an autoregressive moving average model), and a multilayer perceptron neural network model. As it turns out, the proposed methodology produces a higher trading performance, even during the financial crisis period, in terms of annualized return and information ratio, while providing information about the relationship between the ASE20 index and DAX30, NIKKEI225, FTSE100 and S&P500 indices.     

Realizing stock market crashes: stochastic cusp catastrophe model of returns under time-varying volatility

This paper develops a two-step estimation methodology that allows us to apply catastrophe theory to stock market returns with time-varying volatility and to model stock market crashes. In the first step, we utilize high-frequency data to estimate daily realized volatility from returns. Then, we use stochastic cusp catastrophe theory on data normalized by the estimated volatility in the second step to study possible discontinuities in the markets. We support our methodology through simulations in which we discuss the importance of stochastic noise and volatility in a deterministic cusp catastrophe model. The methodology is empirically tested on nearly 27 years of US stock market returns covering several important recessions and crisis periods. While we find that the stock markets showed signs of bifurcation in the first half of the period, catastrophe theory was not able to confirm this behaviour in the second half. Translating the results, we find that the US stock market’s downturns were more likely to be driven by the endogenous market forces during the first half of the studied period, while during the second half of the period, exogenous forces seem to be driving the market’s instability. The results suggest that the proposed methodology provides an important shift in the application of catastrophe theory to stock markets.     

Market illiquidity and bounds on European option prices

The paper analyses the impact of illiquidity of a stock paying no dividends on the pricing of European options written on that stock. In particular, it is shown how illiquidity generates price bounds on an option on this stock, even in the absence of other imperfections, such as transaction costs and trading constraints, or the assumption of stochastic volatility. Moreover, price bounds are shown to be asymmetric with respect to the option price under perfect liquidity. This fact explains, under some conditions, the appearance of a smile effect when the implied volatility is estimated from the mid-quote.     

Coupling index and stocks

In this paper, we are interested in continuous-time models in which the index level induces feedback on the dynamics of its composing stocks. More precisely, we propose a model in which the log-returns of each stock may be decomposed into a systemic part proportional to the log-returns of the index plus an idiosyncratic part. We show that, when the number of stocks in the index is large, this model may be approximated by a local volatility model for the index and a stochastic volatility model for each stock with volatility driven by the index. This result is useful from a calibration perspective: it suggests that one should first calibrate the local volatility of the index and then calibrate the dynamics of each stock. We explain how to do so in the limiting simplified model and in the original model.     

A Utility-Based Model of Common Stock Price Movements

This paper develops and tests a nonlinear utility-based econometric model of the temporal behavior of aggregate stock price movements based on a constant relative risk aversion utility function and an observable information set consisting of aggregate consumption, aggregate dividends, and past stock prices. The stochastic process derived from time-series analyses of consumption and dividends measured over annual intervals is used to derive and empirically test a closed-form solution for stock-price movements. The endogenization of discount rate changes in the utility-based model is shown to be more consistent with aggregate stock price movements over a twenty-year holdout period than constant discount rate models. The model is also used to estimate the representative investor's relative risk aversion. The estimate of 4.22 is consistent with that used by Grossman and Shiller in their perfect foresight model and is significantly higher than the relative risk aversion of 1.0 implied by logarithmic utility.     

沪深300股指期货VaR-GARCH模型风险管理研究——基于恒指期货的比较视角

股指期货是以股票指数作为标的的金融衍生产品,其在金融风险管理中具有重要作用,同时自身也面临较大的风险。VaR—GARCH模型能够较好地模拟金融市场时间序列数据,并作出相应的估计值,是当前主流的风险管理方法。本文基于香港恒指期货的比较视角,对我国去年推出的沪深300股指期货交易进行VaR—GARCH模型实证分析,得出VaR—GARCH模型能够较好地管理沪深300股指期货的风险的结论,并建议加强VaR技术的运用和加强跨市监管,更好地管理股指期货的风险。     

Option Pricing under Stochastic Interest Rates: An Empirical Investigation

Using daily data of the Nikkei 225 index, call option prices and call money rates of the Japanese financial market,a comparison is made of the pricing performance of stock option pricing modelsunder several stochastic interest rate processes proposedby the existing term structure literature.The results show that (1) one option pricing modelunder a specific stochastic interest ratedoes not significantly outperformanother option pricing model under an alternative stochasticinterest rate, and (2) incorporating stochastic interest ratesinto stock option pricing does not contribute to the performanceimprovement of the original Black–Scholes pricing formula.     

Links and interdependence of developed stock markets under global economic crisis conditions

The scope of this article is to determine whether global stock markets behave differently under conditions of economic crisis by studying the interdependence among the price indices of 10 markets, including Dow Jones (DJ), DAX and NIKKEI. The stock markets under examination are those of the USA, Belgium, France, Germany, Greece, Italy, The Netherlands, Spain, the United Kingdom and Japan. The sample includes the logarithmic daily closing prices from 1 January 2000 to 20 February 2009, with a total of approximately 2.385 observations analyzed. The empirical findings suggest that the recent deep crisis has increased dramatically their correlation, thus tightening the existing links. Causality also seems to be affected by the crisis, as DJ and DAX cease to exert a dominant influence on the other stock indices. However, in all the other periods, the findings of previous studies (suggesting that DJ and DAX seriously affect the other indices) were verified, independent of the prevailing bear or bull market conditions.     

Generic pricing of FX,inflation and stock options under stochastic interest rates and stochastic volatility

We consider the pricing of FX, inflation and stock options under stochastic interest rates and stochastic volatility, for which we use a generic multi-currency framework. We allow for a general correlation structure between the drivers of the volatility, the inflation index, the domestic (nominal) and the foreign (real) rates. Having the flexibility to correlate the underlying FX/inflation/stock index with both stochastic volatility and stochastic interest rates yields a realistic model that is of practical importance for the pricing and hedging of options with a long-term exposure. We derive explicit valuation formulas for various securities, such as vanilla call/put options, forward starting options, inflation-indexed swaps and inflation caps/floors. These vanilla derivatives can be valued in closed form under Schöbel and Zhu [Eur. Finance Rev., 1999, 4, 23–46] stochastic volatility, whereas we devise an (Monte Carlo) approximation in the form of a very effective control variate for the general Heston [Rev. Financial Stud., 1993, 6, 327–343] model. Finally, we investigate the quality of this approximation numerically and consider a calibration example to FX and inflation market data.