MAT 4376F/5313F (Winter 2019)
Pro ject
Due date (Project): 30 April 2019
Choose one project. For project number 3, you can work in groups (3 people at most). Send the project by email to rkulik:
Q1. (Only for undergraduate students)
• Download data set swiss (available on the webpage). This data set contains historical exchange rates
between USD and CHF. Compute log-returns: Xt = log St − log St−1, where St are the original values.
• Fit univariate distribution (e.g normal, Pareto, t, exponential). Estimate the parameters. Calculate Value-
At-Risk and Expected-Shortfall.
• Fit ARCH(1) model Yt = σtZt. Estimate the parameters. Compute residuals and fit a distribution to the
noise Zt (e.g. normal or t). Using this, calculate the conditional Value-At-Risk and Expected-Shortfall.
Q2. (Only for graduate students)
• Download data sets swiss and yuan (available on the webpage). These data sets contain historical exchange
rates between USD/CHF and USD/Yuan. Compute log-returns: Xt = log St − log St−1, where St are the
original values. Both data sets have the same length.
• Fit multivariate distribution (multivariate normal or multivariate t). Estimate the parameters. Calculate
Value-At-Risk and Expected-Shortfall for the aggregated portfolio.
Q3. (Group project)
• Download a bivariate data sets. For example, stock prices (recorded on the same days) for two assets (make
sure that both data sets have the same length). Compute log-returns: Xt = log St − log St−1, where St are
the original values.
• Fit multivariate distribution (multivariate normal or multivariate t). Estimate the parameters. Calculate
Value-At-Risk and Expected-Shortfall for the aggregated portfolio.
• Fit ARCH(1) models Yt = σtZt to both series of log-returns. Estimate the parameters. Compute residuals
and fit a distribution to the noise Zt (e.g. normal or t). Using this, calculate the conditional Value-At-Risk and Expected-Shortfall.
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