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P1.T2.401. Time-adjusted efficient estimators in Monte Carlo simulation

Nicole Seaman

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AIMs: Describe the advantages of simulation modeling when multiple input variables and compounding distributions are involved. Interpret discretization error bias and describe how to identify an efficient estimator.


401.1. In arguing in favor of a simulation model approach, Risk Analyst William makes the following five arguments:

I. Neither the sum of normal random variables nor the product of lognormal random variables have closed form (analytical) solutions
II. Simulation enables us to evaluate (approximately) a complex function of a random variable.
III. Simulation enables us to visualize the probability distribution resulting from compounding probability distributions for multiple input variables.
IV. Simulation allows us to incorporate correlations between input variables.
V. Simulation is a low-cost tool for checking the effect of changing a strategy on an output variable of interest.

Which of his arguments is (are) true?

a. I. only
b. IV and V. only
c. I., II. and III.
d. II., III., IV. and V. (but I. is not true)

401.2. Confronted with discretization error bias, which of the following is the most likely remedy ?

a. Substitute a closed-form expression
b. Assume a mean-reverting process
c. Reduce the time interval length and increase the number of steps
d. Increase the time interval length and decrease the number of steps

401.3. Four simulations all produce an identical sample standard deviation, denoted S. Which simulation is the most efficient, if time-adjusted?

a. 1,000 scenarios requiring 1.0 hour
b. 5,000 scenarios requiring 3.0 hours
c. 10,000 scenarios requiring 9.0 hours
d. 30,000 scenarios requiring 25.0 hours

Answers here:
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New Member
Question 401.1 provides the possible answer d as : d. II., III., IV. and IV. (but I. is not true)

I'm quite sure this is a typo.