Monte Carlo Simulation

Monte Carlo simulation involves the use of a computer to represent the operation of a complex financial system.

A characteristic feature is the generation of a large number of random samples from a specified probability distribution or distributions to represent the role of risk in the system.

Uses: planning, developing estimates of VaR, valuing complex securities.

Compared with analytical methods: Provides only statistical estimates, not exact results. Do not directly provide precise insights.

Historical simulation is grounded in actual data but can reflect only risks represented in the sample historical data. Does not lend itself to “what if” analyses.

[Practice Problems] A Monte Carlo simulation can be used to:

A.  directly provide precise valuations of call options.

B.  simulate a process from historical records of returns.

C.  test the sensitivity of a model to changes in assumptions.

[Solutions] C

A characteristic feature of Monte Carlo simulation is the generation of a large number of random samples from a specified probability distribution or distributions to represent the role of risk in the system.

[Practice Problems] A limitation of Monte Carlo simulation is:

A.  its failure to do “what if” analysis.

B.  that it requires historical records of returns

C.  its inability to independently specify cause-and-effect relationships.

[Solutions] C

Monte Carlo simulation is a complement to analytical methods. Monte Carlo simulation provides statistical estimates and not exact results. Analytical methods, when available, provide more insight into cause-and-effect relationships