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# P1.T2.600. Monte Carlo simulation, sampling error (Brooks)

#### Nicole Seaman

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Learning objectives: Describe the basic steps to conduct a Monte Carlo simulation. Describe ways to reduce Monte Carlo sampling error.

Questions:

600.1. Although simulation methods might be employed in each of the following situations (or "use cases"), which situation below LEAST requires the use of a simulation method?

a. Estimating the value of an exotic option when an analytical pricing formula is unavailable
b. Determining the effect on financial markets of substantial changes in the macroeconomic environment
c. Calibrating the size of a Treasury bond trade in order to hedge the duration risk of a corporate bond portfolio
d. Stress-testing a risk management model to determine whether they generate capital requirements sufficient to cover losses in all situations

600.2. Peter the analyst conducted a Monte Carlo simulation in two stages. He presented it to the firm's risk committee, who deemed it useful and robust. In regard to his simulation, each of the following is plausible EXCEPT which is unlikely?

a. In the first stage, the probability distribution specified for errors was not the normal distribution
b. In the second stage, the parameter of interest is a portfolio value rather than a regression coefficient
c. In the first state, a full structural model informed the data generating process (DGP) rather than a pure time series model
d. In the second stage the quantity (N), which is the number of replications, was limited to a low value because the desired confidence was high

600.3. Paul is a researcher who is using Monte Carlo simulation in order to determining what effect heteroscedasticity has upon the size and power of a test for autocorrelation. If the variance of the estimate, var(x), of his quantity of interest is 36.0 and he requires a standard error of the estimate, S(x), to be no greater than 0.10, how many replications does his simulation require?

a. 360
b. 3,600
c. 10,000
c. 36,000