1. Fin250f: Lecture 9 Spring 2010 Brooks, chapter 12.1-12.4 Monte-carlo and Bootstrapping

2. Outline • Computer simulation • Monte-carlo • Bootstrapping

3. Why Simulations? • Small samples • Complex expressions (no analytics) • Ease of use (hard to get analytics)

4. Examples from Finance • Risk management • Value-at-Risk/Stress testing • Option pricing • Trading rules and data snooping • Stationarity testing

5. Monte-carlo procedure • Postulate "data generating process" DGP • Simulate with random number generator y = b*x + e • Estimate b • Store distribution • Examples: simplemc.m, snooprule.m

6. Random Number Generators • Fake random numbers • Random seed to start • Matlab and seeds • newSeed.m

7. Bootstrapping • Use actual data • Draw new set of data independently • Stock returns • Write on paper • Throw in urn • Draw returns at random with replacement • Sample.m • genRandomWalk.m

8. Bootstrapping a Regression • Two methods • Method 1 • Resample (y,x) pairs • Method 2 • Resample e = y-bx residuals • Then regenerate y from scrambled e

9. Power of the Bootstrap • No distributional assumptions • Data speaks for itself

10. Problems with Bootstrap • Outliers in the data • Too little data • Nonstationary data • Nonindependent data • Max's and mins

11. Antithetic Sampling • If distribution is symmetric about zero • Simulate with bootstrap • Randomly flip sign • Like having twice as much data

12. Bootstrap Examples • bootcapm.m • bootquantile.m

13. Monte-carlo Examples • mclinearsnoop.m • In sample/out sample • snooprule.m • Trading rule snooping • Best rules out of a group • mcmse.m