In this chapter, you will learn how to: Design simulation frameworks to solve a variety of problems in finance, explain the difference between pure simulation and bootstrapping, describe the various techniques available for reducing Monte Carlo sampling variability, implement a simulation analysis in EViews. | Chapter 13 Simulation Methods ‘Introductory Econometrics for Finance’ c Chris Brooks 2013 1 Simulation Methods in Econometrics and Finance • The Monte Carlo Method This technique is often used in econometrics when the properties of a particular estimation method are not known. Examples from econometrics include: 1. Quantifying the simultaneous equations bias induced by treating an endogenous variable as exogenous. 2. Determining the appropriate critical values for a Dickey-Fuller test. 3. Determining what effect heteroscedasticity has upon the size and power of a test for autocorrelation. ‘Introductory Econometrics for Finance’ c Chris Brooks 2013 2 Simulation Methods in Econometrics and Finance (Cont’d) Simulations are also often extremely useful tools in finance, in situations such as: 1. The pricing of exotic options, where an analytical pricing formula is unavailable. 2. Determining the effect on financial markets of substantial changes in the macroeconomic environment. 3. “Stress-testing” risk management models to determine whether they generate capital requirements sufficient to cover losses in all situations. ‘Introductory Econometrics for Finance’ c Chris Brooks 2013 3 Conducting Simulations Experiments • In all of the above examples, the basic way that such a study would be conducted (with additional steps and modifications where necessary) is as follows. 1. Generate the data according to the desired data generating process (DGP), with the errors being drawn from some given distribution. 2. Do the regression and calculate the test statistic. 3. Save the test statistic or whatever parameter is of interest. 4. Go back to stage 1 and repeat N times. • N is the number of replications, and should be as large as is feasible. • The central idea behind Monte Carlo is that of random sampling from a given distribution. • Therefore, if the number of replications is set too small, the results will be sensitive to “odd” combinations of random number .
