Robust estimation of historical volatility and correlations in risk management

Financial time series have two features which, in many cases, prevent the use of conventional estimators of volatilities and correlations: leptokurtotic distributions and contamination of data with outliers. Other techniques are required to achieve stable and accurate results. In this paper, we review robust estimators for volatilities and correlations and identify those best suited for use in risk management. The selection criteria were that the estimator should be stable to both fractionally small departures for all data points (fat tails), and to fractionally large departures for a small number of data points (outliers). Since risk management typically deals with thousands of time series at once, another major requirement was the independence of the approach of any manual correction or data pre-processing. We recommend using volatility t-estimators, for which we derived the estimation error formula for the case when the exact shape of the data distribution is unknown. A convenient robust estimator for correlations is Kendall's tau, whose drawback is that it does not guarantee the positivity of the correlation matrix. We chose to use geometric optimization that overcomes this problem by finding the closest correlation matrix to a given matrix in terms of the Hadamard norm. We propose the weights for the norm and demonstrate the efficiency of the algorithm on large-scale problems.     

Log-normal continuous cascade model of asset returns: aggregation properties and estimation

Multifractal models and random cascades have been successfully used to model asset returns. In particular, the log-normal continuous cascade is a parsimonious model that has proven to reproduce most observed stylized facts. In this paper, several statistical issues related to this model are studied. We first present a quick, but extensive, review of its main properties and show that most of these properties can be studied analytically. We then develop an approximation theory in the limit of small intermittency λ²???1, i.e. when the degree of multifractality is small. This allows us to prove that the probability distributions associated with these processes possess some very simple aggregation properties across time scales. Such a control of the process properties at different time scales allows us to address the problem of parameter estimation. We show that one has to distinguish two different asymptotic regimes: the first, referred to as the ‘low-frequency asymptotics’, corresponds to taking a sample whose overall size increases, whereas the second, referred to as the ‘high-frequency asymptotics’, corresponds to sampling the process at an increasing sampling rate. The first case leads to convergent estimators, whereas in the high-frequency asymptotics, the situation is much more intricate: only the intermittency coefficient λ² can be estimated using a consistent estimator. However, we show that, in practical situations, one can detect the nature of the asymptotic regime (low frequency versus high frequency) and consequently decide whether the estimations of the other parameters are reliable or not. We apply our results to equity market (individual stocks and indices) daily return series and illustrate a possible application to the prediction of volatility and conditional value at risk.     

Pairs trading based on statistical variability of the spread process

This research proposes a new non-parametric approach to pairs trading based on renko and kagi constructions which originated from Japanese charting indicators and were introduced to academic studies by Pastukhov. The method exploits statistical information about the variability of the tradable process. The approach does not find a long-run mean of the process and trade towards it like other methods of pairs trading. The only assumption we need is that the statistical properties of the spread process volatility remain reasonably constant. The theoretical profitability of the method has been demonstrated for the Ornstein–Uhlenbeck process. Tests on the daily market data of American and Australian stock exchanges show statistically significant average excess returns ranging from 1.4 to 3.6% per month and annualized Sharpe ratio from 1.5 to 3.4.     

Pricing of vanilla and first-generation exotic options in the local stochastic volatility framework: survey and new results

Stochastic volatility (SV) and local stochastic volatility (LSV) processes can be used to model the evolution of various financial variables such as FX rates, stock prices and so on. Considerable efforts have been devoted to pricing derivatives written on underliers governed by such processes. Many issues remain, though, including the efficacy of the standard alternating direction implicit (ADI) numerical methods for solving SV and LSV pricing problems. In general, the amount of required computations for these methods is very substantial. In this paper, we address some of these issues and propose a viable alternative to the standard ADI methods based on Galerkin-Ritz ideas. We also discuss various approaches to solving the corresponding pricing problems in a semi-analytical fashion. We use the fact that in the zero correlation case some of the pricing problems can be solved analytically, and develop a closed-form series expansion in powers of correlation. We perform a thorough benchmarking of various numerical solutions by using analytical and semi-analytical solutions derived in the paper.     

Enhanced policy iteration for American options via scenario selection

Kolodko and Schoenmakers (2006 Kolodko, A and Schoenmakers, J. 2006. Iterative construction of the optimal Bermudan stopping time. Finan. Stochast., 10: 27–49. [Crossref], [Web of Science ®] , [Google Scholar]) and Bender and Schoenmakers (2006 Bender, C, Kolodko, A and Schoenmakers, J. 2006. Iterating cancelable snowballs and related exotics in a many-factor Libor model. Risk, September: 126–130.  [Google Scholar]) introduced a policy iteration that allows the achievement of a tight lower approximations of the price for early exercise options via a nested Monte Carlo simulation in a Markovian setting. In this paper we enhance the algorithm by a scenario selection method. It is demonstrated by numerical examples that the scenario selection can significantly reduce the number of inner simulations actually performed, and thus can greatly speed up the method (by up to a factor of 15 in some examples). Moreover, it is shown that the modified algorithm retains the desirable properties of the original, such as the monotone improvement property, termination after a finite number of iteration steps, and numerical stability.     

Fast simulations in credit risk

We consider the problem of simulating tail loss probabilities and expected losses conditioned on exceeding a large threshold (expected shortfall) for credit portfolios. Our new idea, called the geometric shortcut, allows an efficient simulation for the case of independent obligors. It is even possible to show that, when the average default probability tends to zero, its asymptotic efficiency is higher than that of the naive algorithm. The geometric shortcut is also useful for models with dependent obligors and can be used for dependence structures modeled with arbitrary copulae. The paper contains the details for simulating the risk of the normal copula credit risk model by combining outer importance sampling with the geometric shortcut. Numerical results show that the new method is efficient in assessing tail loss probabilities and expected shortfall for credit risk portfolios. The new method outperforms all known methods, especially for credit portfolios consisting of weakly correlated obligors and for evaluating the tail loss probabilities at many thresholds in a single simulation run.     

Analysing liquidity and absorption limits of electronic markets with volume durations

This paper focuses on the liquidity of electronic stock markets applying a sequential estimation approach of models for volume duration with increasing threshold values. A modified ACD model with a Box–Tukey transformation and a flexible generalized beta distribution is proposed to capture the changing cluster structure of duration processes. The estimation results with German XETRA data reveal the market's absorption limit for high volumes of shares, expanding the time costs of illiquidity when trading these quantities.     

Modelling spikes and pricing swing options in electricity markets

Most electricity markets exhibit high volatilities and occasional distinctive price spikes, which result in demand for derivative products which protect the holder against high prices. In this paper we examine a simple spot price model that is the exponential of the sum of an Ornstein–Uhlenbeck and an independent mean-reverting pure jump process. We derive the moment generating function as well as various approximations to the probability density function of the logarithm of the spot price process at maturity T. Hence we are able to calibrate the model to the observed forward curve and present semi-analytic formulae for premia of path-independent options as well as approximations to call and put options on forward contracts with and without a delivery period. In order to price path-dependent options with multiple exercise rights like swing contracts a grid method is utilized which in turn uses approximations to the conditional density of the spot process.     

Managing aging workers: a mixed methods study on bundles of HR practices for aging workers

Since abilities and motives change with age and common human resource (HR) practices might be less suitable for aging employees, scholars and practitioners are currently challenged to find new ways of managing aging workers and motivating them to continue working. Therefore, this mixed methods study builds on literature on lifespan development and literature on HR practices in proposing four new bundles of HR practices for aging workers: accommodative, maintenance, utilization and development HR bundles. Since we draw on separate bodies of literature to propose new constructs, we use a mixed methods design in order to triangulate our findings. The proposed HR bundles were explored with a qualitative interview study among HR managers, line managers and employees in the Dutch construction sector, and tested with a quantitative survey study among Dutch government workers. Both studies confirmed that HR practices for aging workers can be classified into accommodative, maintenance, utilization and development HR bundles of practices.     

Decision support systems for human resource training and development

Human resource training and development methods and techniques have different qualitative characteristics that require a multicriteria and multiscenario framework for their assessment. This study incorporates the AHP to assess the nine most important human resource training and development methods and techniques, under five criteria and six scenarios. The methods considered are ‘on-the-job training’, ‘mentorship’, ‘apprenticeship’, ‘vestibule training/simulators’, ‘web-based learning’, ‘instructor-led classroom training’, ‘programmed self-instruction’, ‘case studies/role playing’ and ‘systematic job rotations and transfers’. ‘Vestibule training/simulators’ and ‘mentorship’ have the average best scores, and they should be among the first priorities especially when efficiency, the motivation of employees and minimization of the duration of training time are the most important factors. ‘Web-based learning’ is ideal for minimizing training costs or when ease of application is the first priority. ‘On-the-job training’ is a very good alternative when the cost of training should be reduced while the motivation of employees should be increased.