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Details of Grant 

EPSRC Reference: EP/W005832/1
Title: Hysteresis phenomenon and expected shortfall of financial returns
Principal Investigator: Cai, Dr Y
Other Investigators:
Researcher Co-Investigators:
Project Partners:
Department: School of Management
Organisation: Swansea University
Scheme: Standard Research - NR1
Starts: 31 October 2022 Ends: 29 February 2024 Value (£): 28,928
EPSRC Research Topic Classifications:
Statistics & Appl. Probability
EPSRC Industrial Sector Classifications:
Financial Services
Related Grants:
Panel History:
Panel DatePanel NameOutcome
26 May 2021 EPSRC Mathematical Sciences Small Grants Panel May 2021 Announced
Summary on Grant Application Form
Crouhy and Rockinger (1997) found that bad news increases volatility of stock returns, while good news has a very small impact on volatility except when they are clustered over a few days, which in this case reduces volatility. This suggests that volatility responds to bad and good news differently, and it may remain unchanged even when there is a release of bad or good news unless some other conditions are satisfied as well. We call this phenomenon the hysteresis phenomenon.

To model the hysteresis phenomenon in financial process, Li et al. (2015) proposed a hysteretic AR model. They showed that the hysteresis phenomenon can be modelled by a hysteretic zone, which divides the distribution range of the underlying process into three regimes. The evolution of the process will remain in the hysteretic zone until some other conditions have been satisfied. Zhu et al. (2017) extended the work of Li et al. (2015) to hysteretic AR-GARCH model so that both conditional mean and volatility of the underlying financial process are affected by the hysteresis phenomenon.

It is seen that the hysteresis phenomenon in financial process reflects the relation between a hysteresis zone and the psychology of the markets and the way that traders process financial and economic information. In other words, market participants may stay where they are until they obtain more information that enables them to assess the financial risks that may be caused by the actions they may take.

However, these hysteretic models only focus on the level and volatility of the underlying financial process. Therefore, they can be used for modelling the hysteresis phenomenon, but they may not be suitable for financial risk management. This is because the more appropriate metrics for financial risk management are value-at-risk (VaR) and expected shortfall (ES), rather than level or volatility. In finance, VaR gives the maximum amount expected to be lost over a given time horizon, at a pre-defined confidence level, and ES measures the conditional expectation of loss given that the loss is beyond the VaR level. See e.g. Artzner et al. (1997,1999), Acerbi and Tasche (2002) and Yamai and Yoshiba (2002) and references therein.

In this project, we will focus on the ES of financial returns. Nadarajah et al. (2014) gave an excellent review on the estimation methods for ES, in which more than 150 references were discussed. They showed that one of the common methods for ES estimation is to use the conditional distribution defined by a parametric statistical model. However, the distribution defined by the existing hysteretic models may not capture the much-needed tail-related information for ES estimation. This gives another reason why the existing hysteretic models are not suitable for financial risk management. Note that an example of the information related to the tail is the distributed tail shape. According to the definition of ES, tail shape plays an important role in ES estimation.

Therefore, it is important to know how to model the hysteresis phenomenon in a financial process and how to use the information about the tail shape of the financial process to estimate the ES of the process. Currently, it is not clear how to address these two issues using a single statistical model. This is a gap in the statistical and financial literature. Therefore, this project will fill the gap by developing a novel statistical model based on quantile function, so that the developed model can capture the hysteresis phenomenon in the financial process, and it is also particularly suitable for ES estimation.

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Organisation Website: http://www.swan.ac.uk