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This paper aims to test three parametric models in pricing and hedging higher-order moment swaps. Using vanilla option prices from the volatility surface of the Euro Stoxx 50 Index, the paper shows that the pricing accuracy of these models is very satisfactory under four different pricing error functions. The result is that taking a position in a third moment swap considerably improves the performance of the standard hedge of a variance swap based on a static position in the log-contract and a dynamic trading strategy. The position in the third moment swap is taken by running a Monte Carlo simulation.

This paper undertook empirical tests of three parametric models. The aim of the paper is twofold: assess the pricing accuracy of these models and show how the classical hedge of the variance swap in terms of a position in a log-contract and a dynamic trading strategy can be significantly enhanced by using third-order moment swaps. The pricing accuracy was measured under four different pricing error functions. A Monte Carlo simulation was run to take a position in the third moment swap.

The results of the paper are twofold: the pricing accuracy of the Heston (1993) model and that of two Levy models with stochastic time and stochastic volatility are satisfactory; taking a position in third-order moment swaps can significantly improve the performance of the standard hedge of a variance swap.

The limitation is that these empirical tests are conducted on existing three parametric models. Maybe more critical insights could have been revealed had these tests been conducted in a brand new derivatives pricing model.

This work is 100 per cent original, and it undertook empirical tests of the pricing and hedging accuracy of existing three parametric models.

The purpose of this paper is to perform a relative assessment of performance benchmarks based on alternative asset pricing models to evaluate performance of mutual funds and suggest the best approach in Indian context.

Sample of 237 open-ended Indian equity (growth) schemes from April 2003 to March 2013 is used. Both unconditional and conditional versions of eight performance models are employed, namely, Jensen (1968) measure, three-moment asset pricing model, four-moment asset pricing model, Fama and French (1993) three-factor model, Carhart (1997) four-factor model, Elton et al. (1999) five-index model, Fama and French (2015) five-factor model and firm quality five-factor model.

Conditional version of Carhart (1997) model is found to be the most appropriate performance benchmark in the Indian context. Success of conditional models over unconditional models highlights that fund managers dynamically manage their portfolios.

A significant α generated over and above the return estimated using Carhart’s (1997) model reflects true stock-picking skills of fund managers and it is, therefore, worth paying an active management fee. Stock exchanges and credit rating agencies in India should construct indices incorporating size, value and momentum factors to be used for purpose of benchmarking.

The study adds new evidence as to applicability of established asset pricing models as performance benchmarks in emerging market India. It examines role of higher order moments in explaining mutual fund returns which is an under researched area.

To generalize the traditional 2nd order stochastic perturbation technique for input random variables and fields and to demonstrate for flow problems.

The methodology is based on an n‐th order expansion (perturbation) for input random parameters and state functions around their expected value to recover probabilistic moments of the response. A finite element formulation permits stochastic simulations on irregular meshes for practical applications.

The methodology permits approximation of expected values and covariances of quantities such as the fluid pressure and flow velocity using both symbolic and discrete FEM computations. It is applied to inviscid irrotational flow, Poiseulle flow and viscous Couette flow with randomly perturbed boundary conditions, channel height and fluid viscosity to illustrate the scheme.

The focus of the present work is on the basic concepts as a foundation for extension to engineering applications. The formulation for the viscous incompressible problem can be implemented by extending a 3D viscous primitive variable finite element code as outlined in the paper. For the case where the physical parameters are temperature dependent this will necessitate solution of highly non‐linear stochastic differential equations.

Techniques presented here provide an efficient approach for numerical analyses of heat transfer and fluid flow problems, where input design parameters and/or physical quantities may have small random fluctuations. Such an analysis provides a basis for stochastic computational reliability analysis.

The mathematical formulation and computational implementation of the generalized perturbation‐based stochastic finite element method (SFEM) is the main contribution of the paper.

A common feature of certain kinds of data is a high level of statistical dependence across space and time. This spatial and temporal dependence contains useful information that can be exploited to significantly reduce the uncertainty surrounding local distributions. This chapter develops a methodology for inferring local distributions that incorporates these dependencies. The approach accommodates active learning over space and time, and from aggregate data and distributions to disaggregate individual data and distributions. We combine data sets on Kansas winter wheat yields – annual county-level yields over the period from 1947 through 2000 for all 105 counties in the state of Kansas, and 20,720 individual farm-level sample moments, based on ten years of the reported actual production histories for the winter wheat yields of farmers participating in the United States Department of Agriculture Federal Crop Insurance Corporation Multiple Peril Crop Insurance Program in each of the years 1991–2000. We derive a learning rule that combines statewide, county, and local farm-level data using Bayes’ rule to estimate the moments of individual farm-level crop yield distributions. Information theory and the maximum entropy criterion are used to estimate farm-level crop yield densities from these moments. These posterior densities are found to substantially reduce the bias and volatility of crop insurance premium rates.

The purpose of this paper is to propose a new method for estimating continuous‐time stochastic volatility (SV) models for the S&P 500 stock index process using intraday high‐frequency observations of both the S&P 500 index and the Chicago Board Options Exchange (CBOE) implied (or expected) volatility index (VIX).

A primary purpose of the paper is to provide a framework for using intraday high‐frequency data of both the indices' estimates, in particular, for improving the estimation accuracy of the leverage parameter, that is, the correlation between the two Brownian motions driving the diffusive components of the price process and its spot variance process, respectively.

Finite sample simulation results show that the proposed estimator delivers more accurate estimates of the leverage parameter than do existing methods.

The focus of the paper is on the Heston and non‐Heston leverage parameters.

Finite sample simulation results show that the proposed estimator delivers more accurate estimates of the leverage parameter than do existing methods.

The research findings are important for the analysis of ultra high‐frequency financial data.

The paper provides a framework for using intraday high‐frequency data of both indices' estimates, in particular, for improving the estimation accuracy of the leverage parameter, that is, the correlation between the two Brownian motions driving the diffusive components of the price process and its spot variance process, respectively.

Describes a simple algorithm which has been developed for determining exact moments of top event failure probability from the moments of the basic events in a fault tree. This method requires neither Taylor series expansion of top event failure probability function nor its partial derivates to find these moments. This method has subsequently extended to systems with multistate components. Describes a general algorithm for the purpose. Provides several illustrations to highlight its usefulness.

This paper deals with bispectrum estimation via autoregressive (AR) modelling of a process contaminated by additive Gaussian noise (white and coloured). Two main contributions are provided in this work. First, a comparison between the existing third order recursion (TOR) and the constrained third order mean (CTOM) methods is presented. Basically, the second method is shown to be a smoothing windowed version (i.e. a covariance‐type estimator) of the first one, achieved at the expense of the loss of the recursivity in the AR‐model order. This prior analysis has induced us to develop an alternative scheme to tackle this type of problem, which, while maintaining the main feature of the CTOM method as a covariance type estimator, is a recursive‐in‐order algorithm. This recursivity is obtained carrying out an appropriate minimization procedure of some prediction squared errors also defined here. The paper also compares, by means of simulations, this proposed method and the two existing ones.

More studies have investigated the relation between option measures and stock returns during scheduled corporate events. This study adds to the literature and investigates the informational role of options concerning stock returns following unscheduled corporate news events. The authors focus on individual analysts' recommendation changes rather than consensus revisions, as the recommendation consensus might discard a large amount of potentially valuable information in the aggregation process.

Based on the econometric model, the authors follow Bakshi et al. (2003) to construct the model-free option implied measures. The authors further decompose the implied option variance into upside and downside components. In such a way, the different informational roles of call and put options can be distinguished. A variety of regression analyses are conducted to examine the predictive power of option implied measures, and the ordered probit model is used to test the tipping hypothesis of analyst recommendations.

This study’s results show that the option market impounds the “valuable” firm-specific news; thus, the pre-event option market is strongly related to stock returns around recommendations even though recommendation changes are largely “unscheduled”. At the same time, these results suggest that upside (good) and downside (bad) implied volatilities contain distinctive information on subsequent stock returns.

This study provides new evidence that an increase in upside (downside) volatility around analyst recommendation changes would increase the probability that analysts upgrade (downgrade) the stock. The findings provide implications for investors and risk managers in making investment decisions.

Purpose – The purpose of this chapter is to estimate non-Gaussian distributions by means of Johnson distributions. An empirical illustration on hedge fund returns is detailed.

Methodology/approach – To fit non-Gaussian distributions, the chapter introduces the family of Johnson distributions and its general extensions. We use both parametric and non-parametric approaches. In a first step, we analyze the serial correlation of our sample of hedge fund returns and unsmooth the series to correct the correlations. Then, we estimate the distribution by the standard Johnson system of laws. Finally, we search for a more general distribution of Johnson type, using a non-parametric approach.

Findings – We use data from the indexes Credit Suisse/Tremont Hedge Fund (CSFB/Tremont) provided by Credit Suisse. For the parametric approach, we find that the SU Johnson distribution is the most appropriate, except for the Managed Futures. For the non-parametric approach, we determine the best polynomial approximation of the function characterizing the transformation from the initial Gaussian law to the generalized Johnson distribution.

Originality/value of chapter – These findings are novel since we use an extension of the Johnson distributions to better fit non-Gaussian distributions, in particular in the case of hedge fund returns. We illustrate the power of this methodology that can be further developed in the multidimensional case.