i. Determine the Value-at-Risk (VaR), denominated in Australian dollars, for the portfolios provided below using
1. Variance/covariance (Delta-Normal/Delta Gamma for non-linear positions)
2. Historical Simulation
3. Monte Carlo Simulation
ii. Determine the Expected Tail Loss (ETL), denominated in Australian dollars, for the portfolios provided below using the results from
1. Historical Simulation
2. Monte Carlo Simulation
For each of the methods above, calculate the VaR and ETL (where applicable) for the following parameter sets:
Assumptions:
Variance/Covariance method: use delta-normal/delta-gamma approximation method for non-linear positions.
Monte Carlo simulation: Geometric Brownian motion acceptable (but you may choose to use another process if you wish). Zero drift may also be assumed. For the option positions, consider only risk due to the change in the value of the underlying asset.
Mark-to-Market of positions: standard valuation methods assumed.
All options are assumed to be of European style.
All data required for mark-to-market valuation can be found in the data files (Valuation date: 07/08/2015).
For the option positions assume that the standard deviations provided are constant over the holding period for the purpose of VaR.
Outline of Steps:
1. Determine the risk factors affecting each portfolio. (Note: the set of interest rate data provided consists of many more zero-coupon rates than needed for the portfolios.)
2. Determine the valuation formulae to be used for the positions. Some positions may need to be decomposed into simpler instruments (e.g bonds can be decomposed into equivalent zero coupon bonds).
3. Determine the mark-to-market value of the portfolios on the valuation date.
4. Determine a method for estimating the change in the underlying risk factor (e.g. log(change), discrete change (%))
5. Determine the variance/covariance and correlation matrices for the various portfolios.
6. Proceed with VaR estimation.
Task 1:
You are required to submit the results for the following:
1. Mark-to-market value of the all portfolios.
2. Value-at-Risk for the following portfolios:
Portfolio 1
Portfolio 2
Portfolio 4
Using:
a. Variance/covariance methodology
b. Historical simulation.
with the parameter values below:
(You will need to submit the actual results and the code for producing the results.)
Task 2:
Final Submission of Assignment:
The final results of the assignment should be submitted should be in the form of
1. Written report consisting of :
- A brief description of the methods used in calculating VaR.
- Any additional assumptions made for each VaR method including the method used to measure the changes in risk factors, the technique used to determine the 10-day VaR for each method.
- Full documentation of the VaR results for all individual portfolios and the specified combinations using the various methods as required for the assignment. (See table on page 1 of Assignment)
- A brief analysis and explanation of the variability in the VaR estimates determined using the different methods.
- A brief analysis of the diversified vs. undiversified risk for the combined portfolios.
2. Computer programs/spreadsheets developed and used for the assignment.