Analysis of Asymmetric GARCH Volatility Models with Applications to Margin Measurement

Abstract

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A Comparative Analysis of the Nature of Stock Return Volatility in BRICS and G7 Markets

“…GARCH-M t-Dist. On the other hand, the developed markets findings support the evidence found in previous studies, particularly the US market-Lundblad (2007); Goldman and Shen (2018) and Dicle (2019)-but are contrary to the negative risk premium that has also been observed in the same markets by authors such as Glosten et al (1993); Goyal (2000); Kumar and Dhankar (2010); Aslanidis et al (2016); Wang et al (2017) and Eraker and Wu (2017). The difference may be explained by the different sample period lengths, starting and ending periods and market events covered, methods used and different broad market indices.…”

“…Eraker and Wu (2017) found evidence of a negative risk-return relationship, asymmetry and volatility persistence on the US market from 2006-2013. On the same market, Goldman and Shen (2018), over the period 2002-2017, reported volatility persistence, asymmetry and a positive risk premium. Tsuji (2018) found that standard GARCH and EGARCH models' volatility persistence parameter values decreased when structural breaks were considered.…”

Margin requirements based on a stochastic correlation model

“…In essence, margins should be higher in normal times as their values would depend only on a risk measure, serving as a buffer in case of a stress event (Glasserman & Wu, 2018). Optimizing or defining a trade‐off between risk‐sensitivity and procyclicality has been analyzed by several authors, for example, Murphy et al (2016), Berlinger et al (2019a, 2019b), Goldman and Shen (2020, 2017), Raykov (2014, 2018), and Tambucci (2014). The main takeaway of this literature is that neither a totally risk‐sensitive nor a totally anti‐procyclical margin methodology is optimal, instead this optimal value lies somewhere in between.…”

“…They observe that margin requirements tended to move along with the volatility if the latter was rising, however no such effect was discerned when volatility was on a decline. The remaining studies mostly examined margin requirements via the means of simulations that utilize either historical asset prices or even simulated ones (Goldman & Shen, 2017; Murphy et al, 2016; Murphy & Vause, 2021; Zhang, 2019). In a few studies, the framework rather focuses on theoretical modeling (e.g., Berlinger et al, 2019a; O'Neill & Vause, 2018; Raykov, 2014, 2018).…”

“…In practice, for the purpose of volatility estimation, usually the historical volatility is applied (Heckinger et al, 2016), by quantifying volatility either with equally weighted or exponentially weighted moving average weighted standard deviation. Some scientific papers also use generalized autoregressive conditional heteroscedastic (GARCH) models (e.g., Glasserman & Wu, 2018; Goldman & Shen, 2017, 2020; Li et al, 2021; Murphy et al, 2016).…”