Monte Carlo Simulation and Risk Analysis Flashcards
What is risk analysis?
The process of quantifying the likelihood of undesirable and desirable outcomes.
What is a deterministic investment model?
This model does not change as it does not involve randomness and allows you to calculate future events exactly.
What is a stochastic investment model?
This model forecasts the probability of various outcomes under different conditions using random variables. It predicts outcomes that account for certain levels of unpredictability/randomness.
Does the stochastic model give the same results?
No, every recalculation of the model gives a slightly different result.
Where are simulation models used?
1) Finance- investment planning
2) Marketing- product development
3) Management- project management
What is the Monte Carlo simulation?
This is a stats technique in which a quantity is calculated repeatedly using randomly selected what-if scenarios for each calculation. The simulation results in a full range of possible outcomes and the likelihood of each.
What is the Monte Carlo simulation useful for?
It is often used to assess the impact of uncertainty on a decision. This can include the prob of incurring a financial loss, prob.of running out of inventory etc.
Steps for the Monte Carlo simulation
1) Construct a spreadsheet simulation model to express the relationship between the inputs and outputs using appropriate formulas.
2) Represent the uncertain/variable inputs using probability distributions.
3) An iteration/trial is run which generates a random variable and inputs the variable to produce values of interest.
4) Repeat step 3 thousands of times.
5) This produces a distribution for the output variables.
What are the two main ways to represent step 2?
1)You can use real-life historical data to construct an empirical distribution (frequency histogram).
2) Use of a known statistical distribution such as binomial or normal that fits the real-life data.
What is top-hat sampling?
This is often used for empirical discrete or continuous distributions. It uses random numbers to sample values from the distribution so that the proportion of values in the sample matches the probabilities of each value occurring in the distribution,
What does [ show?
This means that it includes the number following.
What does ( show?
This means that it does not include the number that follows.
Steps for top-hat sampling
1) Calculate the cumulative frequency.
2) Then using the calculated cumulative frequency and (), [] we create the interval of random numbers.
What is the inverse transformation method?
This method works for the probability distributions where you can find the inverse of their cumulative distribution function.
Steps for inverse transformation method
1) Put u equal to the CDF to make the equation u= F(x).
2) Rearrange the equation to make x the subject x= G(u)
3) Let u take the value of the random number in the interval [0,1)
4) Sub u into G(u) which gives us the randomly generated value from our chosen probability distribution.
