Quantitative Methods for Financial Markets

Quantitative Methods for Financial Markets

In this assignment, you are required to analyze the one-day Value-at-risk (VaR) of a market index and write a report of your analysis.
Choose one stock market index of your interest. For example, you can choose the Nikkei 225 from Japan, the Dow Jones 30 from the US, the ASX 200 from Australia, the HANG SENG index from Hong Kong, the FTSE 100 index from the UK, or the DAX performance-index from Germany.
Download daily prices of your chosen index spanning 20 years (for example, from 31 Oct 2000 to 31 Oct 2020) from Yahoo Finance: https://au.finance.yahoo.com/world-indices. Transform the adjustedclose price to daily returns expressed in percentages. Write down a brief description of your data. Present descriptive statistics of the returns, such as mean/variance/skewness/kurtosis.
Divide your data into a 10 year in-sample period and a 10 year out-of-sample period. For example, if your data were from 31 Oct 2000 to 31 Oct 2020, the in-sample period would be from 31 Oct 2000 to 31 Oct 2010, and the out-of-sample period would be from 1 Nov 2010 to 31 Oct 2020.
Fit at least two models to the returns in the in-sample period. Restrict the mean equation to the constant conditional mean, i.e., use rt = µ εt, εt= σtzt, and choose your specification for the conditional variance σt2 and the distribution for the shocks zt. For example, you may choose ARCH(1) and GARCH(1,1). Alternatively, you may choose GARCH(1,1) and TARCH(1,1)-t(ν) Describe the models you choose, state your reasons for choosing these models, present the model estimates, and compare the in-sample fit of your models. If you have estimated more than two models for the in-sample periods, select only two models for out-of-sample forecasting and explain why you selected them.
Compute and present in graph the one-day 1% Value-at-risk (VaR) of your market index in the out-ofsample period. Use the two models you selected from the last step to compute the VaR. Choose one scheme of estimation window. For example, you can choose either fixed window, or rolling window, or recursive window. Justify your choice of the estimation window. Comment on the VaR you obtained from different models.
Limit your word count to 1000 and page number to 3. Be concise, and refrain from using too many equations.

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