Monte-carlo and Bootstrapping

Fin250f: Lecture 9Spring 2010

Brooks, chapter 12.1-12.4

Outline

Computer simulationMonte-carloBootstrapping

Why Simulations?

Small samplesComplex expressions (no analytics)

Ease of use (hard to get analytics)

Examples from Finance

Risk management Value-at-Risk/Stress testing

Option pricingTrading rules and data snooping

Stationarity testing

Monte-carlo procedure

Postulate "data generating process" DGP

Simulate with random number generator y = b*x + e

Estimate bStore distributionExamples: simplemc.m, snooprule.m

Random Number Generators

Fake random numbersRandom seed to startMatlab and seeds

newSeed.m

Bootstrapping

Use actual dataDraw new set of data independentlyStock returns

Write on paper Throw in urn Draw returns at random with replacement

Sample.mgenRandomWalk.m

Bootstrapping a Regression

Two methodsMethod 1

Resample (y,x) pairsMethod 2

Resample e = y-bx residuals Then regenerate y from scrambled e

Power of the Bootstrap

No distributional assumptionsData speaks for itself

Problems with Bootstrap

Outliers in the dataToo little dataNonstationary dataNonindependent dataMax's and mins

Antithetic Sampling

If distribution is symmetric about zero Simulate with bootstrap Randomly flip sign

Like having twice as much data

Bootstrap Examples

bootcapm.mbootquantile.m

Monte-carlo Examples

mclinearsnoop.m In sample/out sample

snooprule.m Trading rule snooping Best rules out of a group

mcmse.m