An example where copulas are fitted to temperature and precipitation data.

Three different versions of a model used for the U.S. Air Force to estimate the total cost of a potential (but fictitious) missile system.

1. Deterministic model, based on point estimates.

2. Incorporation of uncertainty according to the guidelines in the Air Force handbook.

3. Incorporation of explicit correlations between selected inputs according to the guidelines in the Air Force handbook.

This model illustrates one possible simulation of hydroelectric power generation for a 120-month horizon. There are three sources of uncertainty: monthly desired power (as a percentage of the maximum possible output), monthly rainfall, and monthly evaporation. This model is based on Roy L. Nersesian's book https://palisadestage.wpengine.com/books/energy.asp.

This model uses historical mining costs for seven years to project costs for the coming year. The model forecasts line items for the coming year in two very different ways. First, it uses @RISK's Distribution Fitting tool to fit the historical data. This is a reasonable approach, but it can be argued that seven data values are not a sufficient basis for fitting a distribution. The second approach uses a more general distribution, the Trigen distribution. The bottom line is that the choice of input distributions can definitely make a difference in the distributions of the outputs.

Here you will find three different versions of a @RISK model used to value a gold mine lease.

1. A basic @RISK model with uncertainty in the amount of gold mined, the unit cost of extracting it, and the price of gold.

2. Same as the basic model, but provides the owner of the lease the option to abandon it at any time.

3. Same as the abandonment model, but where the Time Series Fit feature is used to fit historical gold prices to a time series process.

This model simulates the daily expenses of a business traveler who faces uncertainty each day on whether he makes a trip, and if so, the miles, miles per hour, miles per gallon, and price per gallon for the trip. Its outputs are total cost and total hours driven for a month, and it uses the RiskCollect function to enable sensitivity analysis of these outputs to inputs of interest, such as the average miles per gallon per trip.

This simple model illustrates how the RiskSimtable function can be used for a quick sensitivity analysis on an input.

Three different versions of an example for modeling costs of risk events.

1. Illustrates one way to model cost from an event which might occur in any of the next 12 months.

2. Illustrates one way to model cost from an event which might occur in each of the next 12 months.

3. Illustrates one way to model costs from any number of events during the year.

This simulation model follows a sample of 200 customers who each begin a year in a certain credit rating category and with a certain amount of credit exposure. By the end of the year, each customer has either defaulted or not, and in case of default, the percentage that can be recovered is uncertain. The simulation finds the total amount of loss from these customers and this total's percentage of the total amount of exposure. Also, it uses the RiskPercentile function at several confidence levels to find the amounts of reserve required to be confident of covering the losses._x000D_

This model illustrates how uncertainties can be built into a financial statement (income statement, balance sheet, cash flows) to make future projections.

When a company develops a new product, the profitability of the product is highly uncertain. Simulation is an excellent tool to estimate the average profitability and riskiness of new products. This example was taken from Chapter 28 of "Financial Models using Simulation and Optimization" by Wayne Winston, published by Palisade Corporation, where a detailed, step-by-step explanation can be found.

You will find two versions of this model:

1. Defining the NPV as an Output.

2. Using Advanced Sensitivity Analysis.

This simple model illustrates two ways variable interest rates on a loan might be simulated. In the first model, the yearly interest rates are generated independently of one another. Each is normally distributed with mean 10% and standard deviation 1%. In the second model, a random walk model, the first interest rate is normally distributed with mean 10% and standard deviation 1%, but each succeeding interest rate is normally distributed with mean equal to the actual previous rate and standard deviation 1%.