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In this paper we introduce a new model, named CARMA(p,q)-Hawkes, as the Hawkes model with exponential kernel implies a strictly decreasing behavior of the autocorrelation function while empirical evidences reject its monotonicity. The proposed model is a Hawkes process where the intensity follows a Continuous Time Autoregressive Moving Average (CARMA) process. We also study the conditions for the stationarity and the positivity of the intensity and the strong mixing property for the increments. Furthermore, we present two estimation case studies based respectively on the likelihood and on the autocorrelation function.

In this paper we consider a portfolio selection problem defined for irregularly spaced observations. We use the Independent Component Analysis for the identification of the dependence structure and continuous-time GARCH models for the marginals. We discuss both estimation and simulation of market prices in a context where the time grid of price quotations differs across assets. We present an empirical analysis of the proposed approach using two high-frequency datasets that provides better out-of-sample results than competing portfolio strategies except for the case of severe market conditions with frequent rebalancements.

We study the dependence structure between the S&P500, the VIX Index, and implicit Interexpectile Differences, that are an alternative measure of implied volatility based on the notion of implicit expectile, recently introduced in Bellini et al. [Implicit expectiles and measures of implied volatility. Quant. Finance, 2018a, 18, 1851–1864]. After filtering the time series of the marginals by ARMA-(E)GARCH models, we fit several parametric families of copulas to the pairwise joint distribution of the residuals, in order to investigate the presence of radial asymmetry and asymptotic tail dependence. We find a negative dependence between S&P500 and both implied volatility indices and a positive dependence between VIX and Interexpectile Differences. The best fitting copulas seem relatively stable over time and display both asymmetry and strong tail dependence, in accordance with the leverage effect.

In this paper we propose a continuous time model for modeling the dynamics of a commodity price. In particular, we focus on the term structure of future prices under the assumption that the underlying asset price follows an exponential CARMA(p, q) model where the driving noise is a Time Changed Brownian motion. The use of CARMA models well suits a market where if a shock occurs its effect does not vanish gradually but it may induce a more complex dynamics for the asset. The obtained formula is strictly connected to the cumulant generating function of the subordinator process in the Time Changed Brownian Motion.

In this paper we show how to approximate the transition density of a CARMA(p,q) model driven by a time-changed Brownian motion based on the Gauss-Laguerre quadrature. This approach allows us to introduce an estimation method that maximizes a likelihood function constructed using the approximated transition density. We also provide formulas for the futures term structures and for prices of options written on futures when the underlying follows an exponential CARMA(p,q) model.

We propose a class of discrete-time stochastic volatility models that, in a parsimonious way, capture the time-varying higher moments observed in financial series. Three desirable results are obtained. First, we have a recursive procedure for the log-price characteristic function which allows a semi-analytical formula for option prices as in Heston and Nandi (Rev Financ Stud 13(3):585–625, 2000). Second, we reproduce some features of the VIX Index. Finally, we derive a simple formula for the VIX index and use it for option pricing.

In this study, the interface between different types of bacteria-embedded self-healing polylactic acid capsules (PLA) and cement paste is investigated. Particularly, the changes in microstructure and mechanical properties of the interface with respect to bulk cement paste were studied. First, nanoindentation was performed to obtain maps of hardness and elastic modulus in the interfaces. Lattice modeling of uniaxial tensile test on the mapped locations was performed then to obtain the overall tensile strength and stiffness of the interface. Moreover, hydrates assemblage and chemical composition around the PLA particles were studied through Backscattering Electron images and Energy Dispersive X-ray Spectroscopy. The ratios between resulting tensile strength and elastic modulus of the interface with respect to bulk paste were obtained for each PLA type. The results suggest that PLA can be tailored to optimize the physico-mechanical properties of the interface and hence, the mechanical behavior and triggering efficiency of the self-healing system., Materials and Environment

In this study, the interface between different types of bacteria-embedded self-healing polylactic acid capsules (PLA) and cement paste is investigated. Particularly, the changes in microstructure and mechanical properties of the interface with respect to bulk cement paste were studied. First, nanoindentation was performed to obtain maps of hardness and elastic modulus in the interfaces. Lattice modeling of uniaxial tensile test on the mapped locations was performed then to obtain the overall tensile strength and stiffness of the interface. Moreover, hydrates assemblage and chemical composition around the PLA particles were studied through Backscattering Electron images and Energy Dispersive X-ray Spectroscopy. The ratios between resulting tensile strength and elastic modulus of the interface with respect to bulk paste were obtained for each PLA type. The results suggest that PLA can be tailored to optimize the physico-mechanical properties of the interface and hence, the mechanical behavior and triggering efficiency of the self-healing system., Materials and Environment

Soft inclusions, such as capsules and other particulate admixtures are increasingly being used in cementitious materials for functional purposes (i.e. self-healing and self-sensing of concrete). Yet, their influence on the fracture behaviour of the material is sometimes overlooked and requires in-depth study for the optimization of mechanical and/or smart properties. An experimental investigation is presented herein on the role of bacteria-based lactate-derived particles on the fracture behaviour of cement paste in tensile configuration. These admixtures are currently used for the purpose of self-healing. Digital Image Correlation was used to obtain strain contours on the surface of the samples during the test. The influence of soft particles addition and age of the samples on the fracture mechanics of the composite were investigated., Materials and Environment

Soft inclusions, such as capsules and other particulate admixtures are increasingly being used in cementitious materials for functional purposes (i.e. self-healing and self-sensing of concrete). Yet, their influence on the fracture behaviour of the material is sometimes overlooked and requires in-depth study for the optimization of mechanical and/or smart properties. An experimental investigation is presented herein on the role of bacteria-based lactate-derived particles on the fracture behaviour of cement paste in tensile configuration. These admixtures are currently used for the purpose of self-healing. Digital Image Correlation was used to obtain strain contours on the surface of the samples during the test. The influence of soft particles addition and age of the samples on the fracture mechanics of the composite were investigated., Materials and Environment

Recent literature on mortality modeling suggests to include in the dynamics of mortality rates the effects of time, age, the interaction of these two and a term for possible shocks. In this paper we investigate models that use Legendre polynomials for the inclusion of age and cohort effects. In order to capture the dynamics of the shock term it is suggested to consider continuous autoregressive moving average (CARMA) models due to their flexibility in reproducing different autoregressive profiles of the shock term. In order to validate the proposed model, different life tables are considered. In particular the male life tables for New Zealand, Taiwan and Japan are used for the presentation of in-sample fitting. Empirical analysis suggests that the inclusion of more flexible models such as higher-order CARMA(p,q) models leads to better in-sample fitting.

This paper investigates the use, in practical financial problems, of the Mixed Tempered Stable distribution both in its univariate and multivariate formulation. In the univariate context, we study the dependence of a given coherent risk measure on the distribution parameters. The latter allows to identify the parameters that seem to have a greater influence on the given measure of risk. The multivariate Mixed Tempered Stable distribution enters in a portfolio optimization problem built considering a real market dataset of seventeen hedge fund indexes. We combine the flexibility of the multivariate Mixed Tempered Stable distribution, in capturing different tail behaviors, with the ability of the ARMA-GARCH model in capturing the time dependence observed in the data.

Recent literature on mortality modeling suggests to include in the dynamics of mortality rates the effect of time, age, the interaction of the latter two terms and finally a term for possible shocks that introduce additional uncertainty.We consider for our analysis models that use Legendre polynomials, for the inclusion of age and cohort effects, and investigate the dynamics of the residuals that we get from fitted models. Obviously, we expect the effect of shocks to be included in the residual term of the basic model. The main finding here is that there is persistence in the residual term but the autocorrelation structure does not display a negative exponential behavior. This empirical result suggests that the inclusion of the additional shock term requires an appropriate model that displays a more flexible autocorrelation structure than the Ornstein-Uhlenbeck employed in existing models.

In this article, we construct a sequence of discrete-time stochastic processes that converges in the Skorokhod metric to a COGARCH(p,q) model. The result is useful for the estimation of the COGARCH(p,q) on irregularly spaced time series data. The proposed estimation procedure is based on the maximization of a pseudo log-likelihood function and is implemented in the yuima package.

We show how to compute the expectiles of the risk-neutral distribution from the prices of European call and put options. Empirical properties of these implicit expectiles are studied on a data-set of closing daily prices of FTSE MIB index options. We introduce the interexpectile difference Delta tau (X) := e(tau) (X) - e(1-tau) (X), for tau is an element of (1/2, 1], and suggest that it is a natural measure of the variability of the risk-neutral distribution. We investigate its theoretical and empirical properties and compare it with the VIX index computed by CBOE

A review of the univariate MixedTS is given and some new results on the asymptotic tail behaviour are derived. The multivariate version of the Mixed Tempered Stable, which is a generalisation of the Normal Variance Mean Mixtures, is discussed. Characteristics of this distribution, its capacity in fitting tails and in capturing dependence structure between components are investigated. We discuss a random number generating procedure and introduce an estimation methodology based on the minimisation of a distance between empirical and theoretical characteristic functions. Asymptotic tail behaviour of the univariate Mixed Tempered Stable is exploited in the estimation procedure in order to obtain a better fitting on tails. Advantages of the multivariate Mixed Tempered Stable distribution are discussed and illustrated via numerical analysis.

In this paper we discuss a detailed methodology for dealing with Risk parity in a parametric context. In particular, we use the Independent Component Analysis for a linear decomposition of portfolio risk factors. Each Independent Component is modeled with the Mixed Tempered Stable distribution. Risk parity optimal portfolio weights are calculated for three risk measures: Volatility, modified Value At Risk and modified Expected Shortfall. Empirical analysis is discussed in terms of out-of-sample performance and portfolio diversification.

In this paper we present an option pricing model based on the assumption that the underlying asset price is an exponential Mixed Tempered Stable Lévy process. We also introduce a new R package called PricingMixedTS that allows the user to calibrate this model using procedures based on loss or likelihood functions.

We propose a conditional Bilateral Gamma model, in which the shape parameters of the Bilateral Gamma distribution have a Garch-like dynamics. After risk neutralization by means of a Bilateral Esscher transform, the model admits a recursive procedure for the computation of the characteristic function of the underlying at maturity, à la Heston and Nandi (Rev Financ Stud 13(3):562-585, 2000). We compare the calibration performance on SPX options with the models of Heston and Nandi (Rev Financ Stud 13(3):562-585, 2000), Christoffersen et al. (J Econom 131(1-2):253-284, 2006) and with a dynamic variance Gamma model introduced in Mercuri and Bellini (J Financ Decis Mak 7(1):37-51, 2011), obtaining promising results. © 2013 Springer-Verlag Berlin Heidelberg.

In this paper we show how to simulate and estimate a COGARCH(p, q) model in the R package yuima. Several routines for simulation and estimation are introduced. In particular, for the generation of a COGARCH(p, q) trajectory, the user can choose between two alternative schemes. The first is based on the Euler discretization of the stochastic differential equations that identify a COGARCH(p, q) model while the second considers the explicit solution of the equations defining the variance process. Estimation is based on the matching of the empirical with the theoretical autocorrelation function. Three different approaches are implemented: minimization of the mean squared error, minimization of the absolute mean error and the generalized method of moments where the weighting matrix is continuously updated. Numerical examples are given in order to explain methods and classes used in the yuima package.

In this paper we show how to simulate and estimate a COGARCH(p, q) model in the R package yuima. Several routines for simulation and estimation are introduced. In particular, for the generation of a COGARCH(p, q) trajectory, the user can choose between two alternative schemes. The first is based on the Euler discretization of the stochastic differential equations that identify a COGARCH(p, q) model while the second considers the explicit solution of the equations defining the variance process. Estimation is based on the matching of the empirical with the theoretical autocorrelation function. Three different approaches are implemented: minimization of the mean squared error, minimization of the absolute mean error and the generalized method of moments where the weighting matrix is continuously updated. Numerical examples are given in order to explain methods and classes used in the yuima package.

In this paper, we investigate empirically the effect of using higher moments in portfolio allocation when parametric and nonparametric models are used. The nonparametric model considered in this paper is the sample approach; the parametric model is constructed assuming multivariate variance gamma (MVG) joint distribution for asset returns.We consider the MVG models proposed by Madan and Seneta (1990), Semeraro (2008) and Wang (2009). We perform an out-of-sample analysis comparing the optimal portfolios obtained using the MVG models and the sample approach. Our portfolio is composed of 18 assets selected from the S&P500 Index and the dataset consists of daily returns observed from 01/04/2000 to 01/09/2011.

In this paper, we introduce a new parametric distribution, the mixed tempered stable. It has the same structure of the normal variance–mean mixtures but the normality assumption gives way to a semi-heavy tailed distribution. We show that, by choosing appropriately the parameters of the distribution and under the concrete specification of the mixing random variable, it is possible to obtain some well-known distributions as special cases. We employ the mixed tempered stable distribution which has many attractive features for modelling univariate returns. Our results suggest that it is flexible enough to accommodate different density shapes. Furthermore, the analysis applied to statistical time series shows that our approach provides a better fit than competing distributions that are common in the practice of finance.

We analyze a methodology for portfolio selection based on the independent component analysis. In this paper parametric and non-parametric approaches are used for capturing the behavior of independent components that generate the distribution of asset returns. Although the setup is quite general, we focus mainly on the numerical issues encountered for parametric models and suggest the inclusion of a penalty function in the optimization problem.

The Mixed Tempered Stable distribution (MixedTS) recently introduced has as special cases parametric distributions used in asset return modelling such as the Variance Gamma (VG) and Tempered Stable. In this paper, we start from this flexible distribution and compare the historical estimates for the two homogeneous risk measures with the quantities obtained using direct numerical integration and the saddle-point approximation. The homogeneity property enables us to go further and look for the most important sources of risk. Although risk decomposition in a parametric context is not straightforward, modified versions of VaR and ES based on asymptotic expansions simplify the problem.

We propose a class of discrete-time stochastic volatility models that, in a parsimonious way, captures the time-varying higher moments observed in financial series. Three desirable results are obtained. First, we have a recursive procedure for the log-price characteristic function which allows a semi-analytical formula for option prices as in Heston and Nandi [2000]. Second, we reproduce some features of the VIX Index. Finally, we derive a simple formula for the VIX index and use it for option pricing.

We propose a class of discrete-time stochastic volatility models that, in a parsimonious way, captures the time-varying higher moments observed in financial series. Three desirable results are obtained. First, we have a recursive procedure for the log-price characteristic function which allows a semi-analytical formula for option prices as in Heston and Nandi [2000]. Second, we reproduce some features of the VIX Index. Finally, we derive a simple formula for the VIX index and use it for option pricing.

We propose a conditional Bilateral Gamma model, in which the shape parameters of the Bilateral Gamma distribution have a Garch-like dynam- ics. After risk neutralization by means of a Bilateral Esscher Transform, the model admits a recursive procedure for the computation of the char- acteristic function of the underlying at maturity, à la Heston and Nandi (2000). We compare the calibration performance on SPX options with the models of Heston and Nandi (2000), Christo¤ersen, Heston and Jacobs (2006) and with a Dynamic Variance Gamma model introduced in Mercuri and Bellini (2011), obtaining promising results

We propose a conditional Bilateral Gamma model, in which the shape parameters of the Bilateral Gamma distribution have a Garch-like dynam- ics. After risk neutralization by means of a Bilateral Esscher Transform, the model admits a recursive procedure for the computation of the char- acteristic function of the underlying at maturity, à la Heston and Nandi (2000). We compare the calibration performance on SPX options with the models of Heston and Nandi (2000), Christo¤ersen, Heston and Jacobs (2006) and with a Dynamic Variance Gamma model introduced in Mercuri and Bellini (2011), obtaining promising results

In this paper we investigate empirically the effect of using higher moments in portfolio allocation when parametric and non parametric models are used. The non parametric model considered, in this paper, is the sample approach while the parametric one is constructed assuming Multivariate Variance Gamma (MVG henceforth) joint distribution for assets returns. We consider the MVG models proposed by Madan and Seneta (1990), Semeraro (2006) and Wang (2009). We perform an out-of-sample analysis comparing the optimal portfolios obtained using the MVG models and the sample approach. Our portfolio is composed of 18 assets selected from the S&P500 Index and the dataset consists in daily returns observed in the period ranging from 01/04/2000 to 01/09/2011.

Several authors have shown the ability of the variance gamma model to correct some biases of the Black-Scholes model. The variance gamma distribution has two additional parameters that allow to capture the skewness and kurtosis observed in financial data. However its density has not got a simple form formula and this implies numerical issues for historical estimation and option pricing. This paper investigates the possibility of approximating the variance gamma distribution to a finite mixture of normals. Therefore, we apply this result to derive a simple historical estimation procedure by means of the Expectation Maximization algorithm and we obtain a simple formula to price a European call option.

In this paper we investigate empirically the effect of using higher moments in portfolio allocation when parametric and non parametric models are used. The non parametric model considered, in this paper, is the sample approach while the parametric one is constructed assuming Multivariate Variance Gamma (MVG henceforth) joint distribution for assets returns. We consider the MVG models proposed by Madan and Seneta (1990), Semeraro (2006) and Wang (2009). We perform an out-of-sample analysis comparing the optimal portfolios obtained using the MVG models and the sample approach. Our portfolio is composed of 18 assets selected from the S&P500 Index and the dataset consists in daily returns observed in the period ranging from 01/04/2000 to 01/09/2011.

Several authors have shown the ability of the variance gamma model to correct some biases of the Black-Scholes model. The variance gamma distribution has two additional parameters that allow to capture the skewness and kurtosis observed in financial data. However its density has not got a simple form formula and this implies numerical issues for historical estimation and option pricing. This paper investigates the possibility of approximating the variance gamma distribution to a finite mixture of normals. Therefore, we apply this result to derive a simple historical estimation procedure by means of the Expectation Maximization algorithm and we obtain a simple formula to price a European call option.

We derive recursive relationships for the m.g.f. of the geometric average of the underlying within some affine Garch models [Heston and Nandi (2000), Christoffersen et al. (2006), Bellini and Mercuri (2007), Mercuri (2008)] and use them for the semi-analytical valuation of geometric Asian options. Similar relationships are obtained for low order moments of the arithmetic average, that are used for an approximated valuation of arithmetic Asian options based on truncated Edgeworth expansions, following the approach of Turnbull and Wakeman (1991). In both cases the accuracy of the semi-analytical procedure is assessed by means of a comparison with Monte Carlo prices. The results are quite good in the geometric case, while in the arithmetic case the proposed methodology seems to work well only in the Heston and Nandi case. © 2011 World Scientific Publishing Company.

The aim of this paper is to investigate the ability of the Dynamic Variance Gamma model, recently proposed by Bellini and Mercuri (2010), to evaluate option prices on the S&P500 index. We also provide a simple relation between the Dynamic Variance Gamma model and the Vix index. We use this result to build a maximum likelihood estimation procedure and to calibrate the model on option data.

The aim of this paper is to investigate the ability of the Dynamic Variance Gamma model, recently proposed by Bellini and Mercuri (2010), to evaluate option prices on the S&P500 index. We also provide a simple relation between the Dynamic Variance Gamma model and the Vix index. We use this result to build a maximum likelihood estimation procedure and to calibrate the model on option data.

We present a new model where the distribution of innovations is a Normal variance-mean mixture. In the model, the mixing process follows an affine Garch model with Gamma innovations, then we obtain a recursive procedure for the characteristic function of the logprices and we evaluate a European call by inverse Fourier Transform. The model admits the Garch model with Gamma innovations and the Variance-Gamma model as special cases.

We present a new model where the distribution of innovations is a Normal variance-mean mixture. In the model, the mixing process follows an affine Garch model with Gamma innovations, then we obtain a recursive procedure for the characteristic function of the logprices and we evaluate a European call by inverse Fourier Transform. The model admits the Garch model with Gamma innovations and the Variance-Gamma model as special cases.

The key problem for option pricing in Garch models is that the risk-neutral distribution of the underlying at maturity is unknown. Heston and Nandi solved this problem by computing the characteristic function of the underlying by a recursive procedure. Following the same idea, Christoffersen, Heston and Jacobs proposed a Garch-like model with inverse Gaussian innovations and recently Bellini and Mercuri obtained a similar procedure in a model with Gamma innovations. We present a model with tempered stable innovations that encompasses both the CHJ and the BM models as special cases. The proposed model is calibrated on S&P500 closing option prices and its performance is compared with the CHJ, the BM and the Heston–Nandi models.

We derive recursive relationships for the m.g.f. of the geometric average of the underlying within some affine Garch models (namely Heston and Nandi 2000, Christoffersen, Heston and Jacobs 2006, Bellini and Mercuri, 2007, Mercuri, 2008) used for the semi-analytical valuation of geometric Asian options. Similar relationships are obtained for low order moments of the distribution of the arithmetic average of the underlying in the same models, that are used for approximate evaluation of arithmetic Asian options (Turnbull and Wakeman 1991). In both cases the accuracy of the semi-analytical procedure is assessed by means of a comparison with Montecarlo prices.

We derive recursive relationships for the m.g.f. of the geometric average of the underlying within some affine Garch models (namely Heston and Nandi 2000, Christoffersen, Heston and Jacobs 2006, Bellini and Mercuri, 2007, Mercuri, 2008) used for the semi-analytical valuation of geometric Asian options. Similar relationships are obtained for low order moments of the distribution of the arithmetic average of the underlying in the same models, that are used for approximate evaluation of arithmetic Asian options (Turnbull and Wakeman 1991). In both cases the accuracy of the semi-analytical procedure is assessed by means of a comparison with Montecarlo prices.

The key problem for option pricing in Garch models is that the risk-neutral distribution of the underlying at maturity is unknown. Heston and Nandi solved this problem by computing the characteristic function of the underlying by a recursive procedure. Following the same idea, Christoffersen, Heston and Jacobs proposed a Garch-like model with inverse Gaussian innovations and recently Bellini and Mercuri obtained a similar procedure in a model with Gamma innovations. We present a model with tempered stable innovations that encompasses both the CHJ and the BM models as special cases. The proposed model is calibrated on S&P500 closing option prices and its performance is compared with the CHJ, the BM and the Heston–Nandi models.