Michael Stein, Svetlozar T. Rachev, Stoyan V. Stoyanov,Frank J. Fabozzi

We use a combination of sophisticated methods to measure the dependence of a sector FoF on the broad stock market, thereby modeling the univariate randomness of the variables adequately as well. A very parsimonious approach is used to allow for updating in high frequencies and on a regular basis using only recent information and therefore small data sets. This allows for a large variety of applications, from risk management and measurement, portfolio optimizations and scenario analyses to investment selection and hedging purposes as examples, the latter being critical for sector FoFs when adequate hedging tools are unavailable.

Sergio Ortobelli, Svetlozar Rachev, Frank J. Fabozzi

We assess stable Paretian models in portfolio theory and risk management. We describe an investor’s optimal choices under the assumption of non-Gaussian distributed equity returns in the domain of attraction of a stable law. In particular, we examine dynamic portfolio strategies with and without transaction costs in order to compare the forecasting power of discrete-time optimal allocations obtained under different stable Paretian distributional assumptions.

Michael Stein, Svetlozar T. Rachev, Stoyan Stoyanov;

This paper presents a framework to portfolio optimization that is superior to the meanvariance approaches utilized for asset allocation. We show how a portfolio with heavily differing asset types in various market phases can be managed efficiently by using a ratio-based portfolio optimization approach and provide a general solution to related optimization problems and the technical challenges arising from them.

Michael Stein and Svetlozar T. Rachev

We aim to answer whether style neutral portfolios build out of value and growth equity / mutual funds are delivering benefits in terms of returns and diversification or whether they result in costly benchmark tracking products. We analyze style-neutral portfolios by building synthetic funds of funds (FoFs) out of both value and growth-oriented equity funds and contrast their properties with the applicable benchmark and with style FoFs.

Young Shin Kim, Svetlozar T. Rachev, Michele Leonardo Bianchi, Frank J. Fabozzi;

In this paper we derive closed-form solutions for the cumulative density function and the average value-at-risk for five subclasses of the infinitely divisible distributions: classical tempered stable distribution, Kim-Rachev distribution, modified tempered stable distribution, normal tempered stable distribution, and rapidly decreasing tempered stable distribution. We present empirical evidence using the daily performance of the S&P 500 for the period January 2, 1997 through December 29, 2006.

Svetlozar T. Rachev, Michael Stein, Wei Sun;

The concept of copula has received growing attention in finance and economics in recent years. From the early days of use in finance over copulas finding their way to Wall Street in a mass market of credit derivatives, this episode of quantitative modelling of markets was also one of euphoria, exaggerations, misperceptions and debates. Bringing tools from the “hardsciences” like mathematics or physics to a “soft-science”, i.e. to use formulas and models for financial markets or the behaviour of market participants always bears a certain portion of model risk. But the complexity and dynamics of financial markets makes it necessary to employ those tools and thereby improve existing methods. The case of copulas in finance is a typical example of how generally appealing and sensible models may cause unforeseen problems and can lead to debates on the applicability of quantitative methods.

Michael Stein and Svetlozar T. Rachev;

The current paper aims at answering whether style neutral portfolios build out of value and growth equity / mutual funds are delivering benefits in terms of returns and diversification or whether they result in costly benchmark tracking products. We analyze style-neutral portfolios by building synthetic funds of funds (FoFs) out of both value- and growth-oriented equity funds and contrast their properties with the applicable benchmark and with style FoFs. While a beneficial effect with respect to diversification and a resulting reduction in return dispersion can be seen, the simulated FoFs do not deliver a general risk-adjusted outperformance against the benchmark or the better performing style of a period. The variety of results is indicating that FoFs may indeed benefit from investing in a style-neutral portfolio of growth and value funds, but only given that FoF managers are able to select the wellperforming funds of the respective styles. In addition, we find that being able to shift between styles over time may lead to better results than locking in FoFs at being style neutral.

Young Shin Kim, Svetlozar T. Rachev, Michele Leonardo Bianchi, Frank J. Fabozzi;

In this paper, we introduce a new GARCH model with an infinitely divisible distributed innovation, referred to as the rapidly decreasing tempered stable (RDTS) GARCH model. This model allows the description of some stylized empirical facts observed for stock and index returns, such as volatility clustering, the non-zero skewness and excess kurtosis for the residual distribution. Furthermore, we review the classical tempered stable (CTS) GARCH model, which has similar statistical properties.

Ekaterina N. Sereda, Svetozar T. Rachev, Efim M. Bronshtein, Wei Sun, Stoyan Stoyanov, Frank J. Fabozzi

Distortion risk measures are perspective risk measures because they allow an asset manager to reflect a client’s attitude toward risk by choosing the appropriate distortion function. In this paper, the idea of asymmetry was applied to the standard construction of distortion risk measures. The new asymmetric distortion risk measures are derived.

Georgi K. Mitov, Svetlozar T. Rachev, Young Shin Kim, Frank J. Fabozzi

We examine the pricing of barrier options when the price of the underlying asset is modeled by branching process in random environment (BPRE). We derive an analytical formula for the price of an up-and-out call option, one form of a barrier option. Calibration of the model parameters is performed using market prices of standard call options.

Wei Sun, Svetlozar Rachev, Ye Chen, Frank J. Fabozzi

The value at risk (VaR) measure often relies on an assumption about the return (or price) distribution of the underlying risky assets. Different distributional assumptions may produce widely different computed VaR values. When estimating VaR using intra-daily equity returns, the question arises as to what assumption should be made about the return distribution. Because of the difficulty of decomposing trading noise, it is very hard to identify the return distribution at the tick-by-tick level. In this paper, we circumvent the difficulty of making a distributional assumption of intra-daily market fluctuations by specifying a neural network approach.

Stoyan V. Stoyanov, Borjana Racheva-Iotova, Svetlozar T. Rachev; Frank J. Fabozzi

The problem of portfolio risk estimation in volatile markets requires employing fat-tailed models for financial instrument returns combined with copula functions to capture asymmetries in dependence and a true downside risk measure for risk estimation. In this survey, we discuss how these three essential components can be combined together in a Monte Carlo based framework for risk estimation and risk budgeting with the average value-at-risk measure (AVaR). We consider in detail the questions of AVaR calculation and estimation and also stochastic stability of AVaR when combined with heavy-tailed scenarios.

Michael Stein, Svetlozar T. Rachev, Stoyan V. Stoyanov, Frank J. Fabozzi

We use a combination of sophisticated methods to measure the dependence of a sector FoF on the broad stock market, thereby modeling the univariate randomness of the variables adequately as well. A very parsimonious approach is used to allow for updating in high frequencies and on a regular basis using only recent information and therefore small data sets. This allows for a large variety of applications, from risk management and measurement, portfolio optimizations and scenario analyses to investment selection and hedging purposes as examples, the latter being critical for sector FoFs when adequate hedging tools are unavailable.

Sergio Ortobelli, Svetlozar T. Rachev, Haim Shalit, Frank J. Fabozzi

We examine three portfolio-type problems where investors rank their choices considering each of the following: (1) risk, (2) uncertainty, and (3) the distance from a benchmark. For each problem, we analyze possible orderings for the choices and we propose several admissible portfolio optimization problems. Thus, we discuss the properties of several ─ risk measures, uncertainty measures and tracking error measures ─ and their consistency with investor choices. Furthermore, we propose several linearizable allocation problems consistent with a given ordering and demonstrate how many portfolio selection problems proposed in literature can be solved.

Ivan K. Mitov, Svetlozar T. Rachev, Frank J. Fabozzi

The loss distribution approach (LDA) is one of the three advanced measurement approaches (AMA) to the Pillar I modelling proposed by Basel II in 2001. In this paper, one possible approximation of the aggregate and maximum loss distribution in the extremely Low Frequency/High Severity case, i.e. the case of in¯nite mean of the loss sizes and loss inter-arrival times.

Michele Leonardo Bianchi, Svetlozar T. Rachev, Young Shin K, Frank J. Fabozzi

We construct the new class of tempered infinitely divisible (TID) distributions. Taking into account the tempered stable distribution class, as introduced by in the seminal work of Rosinsky, a modification of the tempering function allows one to obtain suitable properties. In particular, TID distributions may have exponential moments of any order and conserve all proper properties of the Rosi´nski setting. Furthermore, we prove that the modified tempered stable distribution is TID and give some further parametric example.

Audrius Kabasinskas, Svetlozar T. Rachev, Leonidas Sakalauska, Wei Sun, Igoris Belovas

Statistical models of financial data series and algorithms of forecasting and investment are the topic of this research. The objects of research are the historical data of financial securities, statistical models of stock returns, parameter estimation methods, effects of self-similarity and multifractality, and algorithms of financial portfolio selection. The numerical methods (MLE and robust) for parameter estimation of stable models have been created and their eciency were compared.

Michele Leonardo Bianchi, Svetlozar T. Rachev, Young Shin Kim, Frank J. Fabozzi

Most of the important models in finance rest on the assumption that randomness is explained through a normal random variable. However there is ample empirical evidence against the normality assumption, since stock returns are heavy-tailed, leptokurtic and skewed.Partly in response to those empirical inconsistencies relative to the properties of the normal distribution, a suitable alternative distribution is the family of tempered stable distributions.In this paper, we address some numerical issues resulting from tempered stable modelling, with a view toward the density approximation and simulation.

Svetlozar T. Rachev, Young Shin Kim, Dong Myung Chung, Michele Leonardo Bianchi

We introduce a new variant of the tempered stable distribution, named the modified tempered stable (MTS) distribution and we develop a GARCH option pricing model with MTS innovations. This model allows the description of some stylized empirical facts observed in financial markets, such as volatility clustering, skewness, and heavy tails of stock returns. To demonstrate the advantages of the MTS-GARCH model, we present the results of the parameter estimation.

Michael Stein, Svetlozar T. Rachev, Wei Sun

We provide a review of developments in the fund of funds (FoF)industry as well as related academic research work. Being portfolios built out of other portfolios and assets, FoFs are a special type of investments and therefore have distinct advantages and disadvantages in comparison with other investment vehicles. When reviewing both the academic research related to the unique, or at least distinct, features of FoFs and discussing market developments, we address a good number of interesting questions and challenges.

Svetlozar T. Rachev, Borjana Racheva-Iotova, Stoyan V. Stoyanov, Frank J. Fabozzi

We describe a framework of a system for risk estimation and portfolio optimization based on stable distributions and the average value-at-risk risk measure. In contrast to normal distributions, stable distributions capture the fat tails and the asymmetric nature of real-world risk factor distributions. In addition, we make use of copulas, a generalization of overly restrictive linear correlation models, to account for the dependencies between risk factors during extreme events.

Our foundation paper introduces a practical alternative to Gaussian risk factor distributions based on Svetlozar Rachev’s work on Stable Paretian Models in Finance (see Rachev and Mittnik, 2000) and called the Stable Distribution Framework. In contrast to normal distributions, stable distributions capture the fat tails and the asymmetries of real-world risk factor distributions. In addition, we make use of copulas, a generalization of overly restrictive linear correlation models, to account for the dependencies between risk factors during extreme events, and multivariate ARCH-type processes with stable innovations to account for joint volatility clustering. We demonstrate that the application of these techniques results in more accurate modeling of extreme risk event probabilities, and consequently delivers more accurate risk measures for both trading and risk management.