Browsing by Subject "skewness"

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  • Karttunen, Henri (2020)
    We define a nonlinear autoregressive time series model based on the generalized hyperbolic distribution in an attempt to model time series with non-Gaussian features such as skewness and heavy tails. We show that the resulting process has a simple condition for stationarity and it is also ergodic. An empirical example with a forecasting experiment is presented to illustrate the features of the proposed model.
  • Kulp-Tåg, Sofie (Svenska handelshögskolan, 2007)
    Working Papers
    This paper examines how volatility in financial markets can preferable be modeled. The examination investigates how good the models for the volatility, both linear and nonlinear, are in absorbing skewness and kurtosis. The examination is done on the Nordic stock markets, including Finland, Sweden, Norway and Denmark. Different linear and nonlinear models are applied, and the results indicates that a linear model can almost always be used for modeling the series under investigation, even though nonlinear models performs slightly better in some cases. These results indicate that the markets under study are exposed to asymmetric patterns only to a certain degree. Negative shocks generally have a more prominent effect on the markets, but these effects are not really strong. However, in terms of absorbing skewness and kurtosis, nonlinear models outperform linear ones.
  • Lindqvist, Thomas; Söderman, Ronnie (Svenska handelshögskolan, 2000)
    Working Papers
    In this paper, we examine the predictability of observed volatility smiles in three major European index options markets, utilising the historical return distributions of the respective underlying assets. The analysis involves an application of the Black (1976) pricing model adjusted in accordance with the Jarrow-Rudd methodology as proposed in 1982. Thereby we adjust the expected future returns for the third and fourth central moments as these represent deviations from normality in the distributions of observed returns. Thus, they are considered one possible explanation to the existence of the smile. The obtained results indicate that the inclusion of the higher moments in the pricing model to some extent reduces the volatility smile, compared with the unadjusted Black-76 model. However, as the smile is partly a function of supply, demand, and liquidity, and as such intricate to model, this modification does not appear sufficient to fully capture the characteristics of the smile.
  • Miettinen, Jarkko (2007)
    In GARCH literature a symmetric conditional probability distribution is often assumed. As the financial data, such as stock market returns, often have both peaked and skewed distribution, this assumption can be too restrictive. We expand this by allowing for the conditional distribution to be asymmetric or skewed. Four distributions that have a normal variance-mean mixture representation are considered. Three of these distributions belong to the class of generalized hyperbolic (GH) distributions. The GH distribution is obtained by assuming that the (unobserved) mixing variable has the generalized inverse Gaussian (GIG) distribution. As the GH distribution is regarded as too broad for GARCH modeling we employ its three special cases. These distributions are obtained by assuming that the mixing distribution has inverse Gaussian (IG), Gamma or reciprocal Gamma (RG) distribution. Resulting distributions are called normal inverse Gaussian (NIG), normal Gamma (NG) and normal reciprocal Gamma (NRG) distributions. In addition, we apply the so-called z distribution. This distribution is obtained by assuming that the mixing distribution has infinite convolution of exponentially distributed random variables. In empirical applications employing two real stock market indices, it was first discovered that statistically significant estimates of the parameters of the skewed distributions were actually obtained. Especially, all the estimates implied negatively skewed conditional distributions. Most of the models based on skewed conditional distributions were also superior to the model based on the symmetric t distribution according to standard model selection criteria. According to plots of the densities of the standardized residuals against the theoretical densities, skewed distributions have better ability to capture the tail behaviour of the financial data than the symmetric t distribution. Advantages of the skewed distributions were also observed through Value-at-Risk (VaR) applications, where the correct shape of the (left) tail of the distribution is of concern. We conclude that allowing for conditional skewness should be taken into consideration in GARCH modeling. The GARCH-in-Mean model with z distribution was introduced by Lanne and Saikkonen (2007). Generalized hyperbolic distributions are overviewed for example in Eberlein and v. Hammerstein (2003). The calculation of the modified Bessel functions was enabled by Abramowitz and Stegun (1970) and especially Spanier and Oldham (1987).
  • Kulp-Tåg, Sofie (Svenska handelshögskolan, 2008)
    Economics and Society
    Financial time series tend to behave in a manner that is not directly drawn from a normal distribution. Asymmetries and nonlinearities are usually seen and these characteristics need to be taken into account. To make forecasts and predictions of future return and risk is rather complicated. The existing models for predicting risk are of help to a certain degree, but the complexity in financial time series data makes it difficult. The introduction of nonlinearities and asymmetries for the purpose of better models and forecasts regarding both mean and variance is supported by the essays in this dissertation. Linear and nonlinear models are consequently introduced in this dissertation. The advantages of nonlinear models are that they can take into account asymmetries. Asymmetric patterns usually mean that large negative returns appear more often than positive returns of the same magnitude. This goes hand in hand with the fact that negative returns are associated with higher risk than in the case where positive returns of the same magnitude are observed. The reason why these models are of high importance lies in the ability to make the best possible estimations and predictions of future returns and for predicting risk.
  • Penttinen, Aku (Svenska handelshögskolan, 2000)
    Working Papers
    Although empirical evidence suggests the contrary, many asset pricing models assume stock returns to be symmetrically distributed. In this paper it is argued that the occurrence of negative jumps in a firm's future earnings and, consequently, in its stock price, is positively related to the level of network externalities in the firm's product market. If the ex post frequency of these negative jumps in a sample does not equal the ex ante assessed probability of occurrence, the sample is subject to a peso problem. The hypothesis is tested for by regressing the skewness coefficient of a firm’s realised stock return distribution on the firm’s R&D intensity, i.e. the ratio of the firm’s research and development expenditure to its net sales. The empirical results support the technology-related peso problem hypothesis. In samples subject to such a peso problem, the returns are biased up and the variance is biased down.