Search results for: GARCH

Authors: Rachid Belhachemi, Pierre Rostan, Alexandra Rostan

Abstract:

This paper develops a discrete-time option pricing model for index options. The model consists of two key ingredients. First, daily stock return innovations are driven by a continuous hidden threshold mixed skew-normal (HTSN) distribution which generates conditional non-normality that is needed to fit daily index return. The most important feature of the HTSN is the inclusion of a latent state variable with a continuum of states, unlike the traditional mixture distributions where the state variable is discrete with little number of states. The HTSN distribution belongs to the class of univariate probability distributions where parameters of the distribution capture the dependence between the variable of interest and the continuous latent state variable (the regime). The distribution has an interpretation in terms of a mixture distribution with time-varying mixing probabilities. It has been shown empirically that this distribution outperforms its main competitor, the mixed normal (MN) distribution, in terms of capturing the stylized facts known for stock returns, namely, volatility clustering, leverage effect, skewness, kurtosis and regime dependence. Second, heteroscedasticity in the model is captured by a threeexogenous-factor GARCH model (GARCHX), where the factors are taken from the principal components analysis of various world indices and presents an application to option pricing. The factors of the GARCHX model are extracted from a matrix of world indices applying principal component analysis (PCA). The empirically determined factors are uncorrelated and represent truly different common components driving the returns. Both factors and the eight parameters inherent to the HTSN distribution aim at capturing the impact of the state of the economy on price levels since distribution parameters have economic interpretations in terms of conditional volatilities and correlations of the returns with the hidden continuous state. The PCA identifies statistically independent factors affecting the random evolution of a given pool of assets -in our paper a pool of international stock indices- and sorting them by order of relative importance. The PCA computes a historical cross asset covariance matrix and identifies principal components representing independent factors. In our paper, factors are used to calibrate the HTSN-GARCHX model and are ultimately responsible for the nature of the distribution of random variables being generated. We benchmark our model to the MN-GARCHX model following the same PCA methodology and the standard Black-Scholes model. We show that our model outperforms the benchmark in terms of RMSE in dollar losses for put and call options, which in turn outperforms the analytical Black-Scholes by capturing the stylized facts known for index returns, namely, volatility clustering, leverage effect, skewness, kurtosis and regime dependence.

Keywords: continuous hidden threshold, factor models, GARCHX models, option pricing, risk-premium

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Authors: Kanokwan Chancharoenchai

Abstract:

Economic growth can be considered as an important element of countries’ development process. For developing countries, like Thailand, to ensure the continuous growth of the economy, the Thai government usually implements various policies to stimulate economic growth. They may take the form of fiscal, monetary, trade, and other policies. Because of these different aspects, understanding factors relating to economic growth could allow the government to introduce the proper plan for the future economic stimulating scheme. Consequently, this issue has caught interest of not only policymakers but also academics. This study, therefore, investigates explanatory variables for economic growth in Thailand from 2005 to 2017 with a total of 52 quarters. The findings would contribute to the field of economic growth and become helpful information to policymakers. The investigation is estimated throughout the production function with non-linear Cobb-Douglas equation. The rate of growth is indicated by the change of GDP in the natural logarithmic form. The relevant factors included in the estimation cover three traditional means of production and implicit effects, such as human capital, international activity and technological transfer from developed countries. Besides, this investigation takes the internal and external instabilities into account as proxied by the unobserved inflation estimation and the real effective exchange rate (REER) of the Thai baht, respectively. The unobserved inflation series are obtained from the AR(1)-ARCH(1) model, while the unobserved REER of Thai baht is gathered from naive OLS-GARCH(1,1) model. According to empirical results, the AR(|2|) equation which includes seven significant variables, namely capital stock, labor, the imports of capital goods, trade openness, the REER of Thai baht uncertainty, one previous GDP, and the world financial crisis in 2009 dummy, presents the most suitable model. The autoregressive model is assumed constant estimator that would somehow cause the unbias. However, this is not the case of the recursive coefficient model from the state space model that allows the transition of coefficients. With the powerful state space model, it provides the productivity or effect of each significant factor more in detail. The state coefficients are estimated based on the AR(|2|) with the exception of the one previous GDP and the 2009 world financial crisis dummy. The findings shed the light that those factors seem to be stable through time since the occurrence of the world financial crisis together with the political situation in Thailand. These two events could lower the confidence in the Thai economy. Moreover, state coefficients highlight the sluggish rate of machinery replacement and quite low technology of capital goods imported from abroad. The Thai government should apply proactive policies via taxation and specific credit policy to improve technological advancement, for instance. Another interesting evidence is the issue of trade openness which shows the negative transition effect along the sample period. This could be explained by the loss of price competitiveness to imported goods, especially under the widespread implementation of free trade agreement. The Thai government should carefully handle with regulations and the investment incentive policy by focusing on strengthening small and medium enterprises.

Keywords: autoregressive model, economic growth, state space model, Thailand

Procedia PDF Downloads 122