FIN 285a: Computer Simulations and Risk Assessment

Blake LeBaron

Fall 2011

Group Project Ideas

1. If the central limit theorem holds then longer horizon returns should be closer to normality. Test the normality assumption on progressively longer geometric returns.
2. Are VaR measures significantly different for blocked versus IID bootstraps. Test this difference by drawing a large number of simulations, and perform a simple t-test on the mean difference. Do this for a few different horizon values.
3. How important is adjusting for overlapping and nonoverlapping returns in long horizon VAR's. Explore this with a monte-carlo of daily returns. In one case try getting a historical VAR using 10 day returns sampled every day. In another case look at 10 day returns sampled daily.
4. Look at volatility adjusted VaR estimated using the risk metrics method. Find the properties of VaR exceptions. Especially, report the autocorrelations of VaR exceptions at lags 1-5.
5. Try implementing a really simple bond pricing model. Assume a 2 year maturity, and a simple 1000 princ. for the bond. Now assume the 1 year interest rate is 3% today with a flat term structure, but it will go up our down by some percentage over the next year. What is the VaR on a portfolio holding this bond?
6. Try implementing a form of block bootstrap for portfolios of returns.
7. Compare a changing volatility to a constant volatility VaR in terms of the cost of reserves set aside. Use some of our Dow data examples, and then assume that firms are required to hold the 95% confidence VaR in terms of reserves. The cost of holding these in cash is some kind of forgone return, so the actual cost would r*reserves, where r is the return. Compare the sum of daily reserve holdings from either the changing VaR or the constant VaR cases to see which is cheaper. (You get to choose r here. Maybe a couple of different guesses would be useful.)
8. Extend the pairs trading example from the last problem set by exploring the impact of increased capital. Try the experiment of increasing the capital floor, and plot how this effects the distribution (in terms of mean and variance) of the final portfolio value.
9. Those who have had options (or maybe those who haven't) might want to expand on any of our options pricing examples by changing the strike price.
10. Extreme value distributions: Try using these in some various VaR estimations.
11. Try out some of the realized volatility measures as compared with ViX and high/low range information. (This are Realized volatility web page.)
12. Further compare the Gaussian copula for portfolio VaR levels and compare with bootstrap, and the multivariate normal. How do they compare for generating co extremes in returns series?
13. In class we used a 5 day moving average with high/low range estimates on volatility. Try varying this from 1 to 20 and see how this effects your results.
14. Further analyze data from last year to see how unusual it is. Report statistics like the VaR over the year, and the number of large returns (greater than 3%). How do these compare with the historical record of the Dow? Also, try looking at returns normalized by the conditional standard deviation. How do these compare with similarly adjusted historical returns.
15. Try redoing the mortgage code for different default probabilities. Also, document the sensitivity to correlation assumptions. Finally, you can explore other recovery rates.
16. Try estimating a changing correlation in the international returns data. Do this with a rolling estimate of the variance covariance matrix. Try estimating a VaR using a simulated multivariate normal with this changing variance covariance matrix.
17. Experiment with different copulas in the mortgage problem.
18. Explore the VaR in the barrier option as the barrier value changes. Plot this for several barrier values.
19. Try barrier option example with an expected shortfall calculation.