Estimating Dependences and Risk between Gold Prices and S&P500: New Evidences from ARCH,GARCH, Copula and ES-VaR models

PhD Thesis

Khan, S. (2022). Estimating Dependences and Risk between Gold Prices and S&P500: New Evidences from ARCH,GARCH, Copula and ES-VaR models. PhD Thesis London South Bank University School of Business
AuthorsKhan, S.
TypePhD Thesis

This thesis examines the correlations and linkages between the stock and commodity in order to quantify the risk present for investors in financial market (stock and commodity) using the
Value at Risk measure. The risk assessed in this thesis is losses on investments in stock (S&P500) and commodity (gold prices). The structure of this thesis is based on three empirical chapters. We emphasise the focus by acknowledging the risk factor which is the non-stop fluctuation in the prices of commodity and stock prices. The thesis starts by measuring volatility, then dependence which is the correlation and lastly measure the expected shortfalls and Value at risk (VaR). The research focuses on mitigating the risk using VaR measures and assessing the use of the volatility measures such as ARCH and GARCH and basic VaR calculations, we also measured the correlation using the Copula method. Since, the measures of volatility methods have limitations that they can measure single security at a time, the second empirical chapter measures the interdependence of stock and commodity (S&P500 and Gold Price Index) by investigating the risk transmission involved in investing in any of them and whether the ups and downs in the prices of one effect the prices of the other using the Time Varying copula method. Lastly, the third empirical chapter which is the last chapter, investigates the expected shortfalls and Value at Risk (VaR) between the S&P500 and Gold prices Index using the ES-VaR method proposed by Patton, Ziegel and Chen (2018). Volatility is considered to be the most popular and traditional measure of risk. For which we have used ARCH and GARCH model in our first empirical chapter. However, the problem with volatility is that it does not take into account the direction of an investments’ movement: volatility of stocks is that they suddenly jump higher and investors are not distressed with gains. When we talk about investors for them the risk is about the odds of losing money, after my research and findings VaR is based on the common-sense fact. Hence, investors care about the odds of big losses, VaR answers the question, what is my worst-case scenario? Or simply how much I could lose in a really bad month? The results of the thesis demonstrated that measuring volatility (ARCH GARCH) alone was not sufficient in measuring the risk involved in an investment therefore
methodologies such as correlation and VAR demonstrates better results. In terms of measuring the interdependence, the Time Varying Copula is used since the dynamic structure of the de-
pendence between the data can be modelled by allowing either the copula function or the dependence parameter to be time varying. Lastly, hybrid model further demonstrates the average return on a risky asset for which Expected Shortfall (ES) along with some quantile dependence and VaR (Value at risk) is utilised. Basel III Accord which is applied in coming years till 2019 focuses more on ES unlike VaR, hence there is little existing work on modelling ES. The thesis focused on the results from the model of Patton, Ziegel and Chen (2018) which is based on the statistical decision theory. Patton, Ziegel and Chen (2018), overcame the problem of elicitability for ES by using ES and VaR jointly and propose the new dynamic model of risk measure. This research adds to the contribution of knowledge that measuring risk by using volatility is not enough for measuring risk, interdependence helps in measuring the dependency of one variable over the other and estimations and inference methods proposed by Patton, Ziegel and Chen (2018) using simulations proposed in ES-VaR model further concludes that ARCH and GARCH or other rolling window models are not enough for determining the risk forecasts. The results suggest, in first empirical chapter we see volatility between Gold prices and S&P500. The second empirical chapter results suggest conditional dependence of the two indexes is strongly time varying. The correlation between the stock is high before 2008. The results further displayed slight stronger bivariate upper tail, which signifies that the conditional dependence of the indexes is influence by positive shocks. The last empirical chapter findings
proposed that measuring forecasts using ES-Var model proposed by Patton, Ziegel and Chen (2018) does outer perform forecasts based on univariate GARCH model. Investors want to 10
protect themselves from high losses and ES-VaR model discussed in last chapter would certainly help them to manage their funds properly.

PublisherLondon South Bank University
Digital Object Identifier (DOI)
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Publication dates
Print24 Aug 2022
Publication process dates
Deposited10 Nov 2022
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