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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%.
This model illustrates variance at risk (VAR) in the context of a put on a stock. It follows two portfolios: one where the investor purchases shares of the stock and no puts, and one where the investor purchases shares of the stock and a put on the stock. Simulation shows that clearly how put acts as a hedge on the stock. The VAR with the put is about a 19.8% loss, compared to a 33.9% loss without the put.
Anybody who owns a portfolio of investments knows there is a great deal of uncertainty about the future worth of the portfolio. Recently the concept of value at risk (VAR) has been used to help describe a portfolio's uncertainty. Simply stated, value at risk of a portfolio at a future point in time is usually considered to be the fifth percentile of the loss in the portfolio's value at that point in time. The following example shows how @RISK can be used to measure VAR. The example also demonstrates how buying puts can greatly reduce the risk in a stock.
This example was taken from Chapter 62 of Financial Models using Simulation and Optimization by Wayne Winston, published by Palisade Corporation, where a detailed, step-by-step explanation can be found.
This model, really a template, is used to value European stock options: calls and/or puts. The model uses the well-known lognormal model of stock price changes to simulate the future stock price. This formula depends on the time till expiration, the riskfree rate, and the volatility of the stock, as well as a standard normal variate.
A Markov chain is a process observed through time where the probability distribution of the next state of the process, given the current state, is independent of the past states. This model illustrates the evolution of prices through time.
The purpose of this model is to provide a comparison between building an onshore plant in the U.S. and building an offshore plant in China. The model is for a company based in the U.S. with sales in the U.S. However, despite transportation costs, there might be benefits to building in China. The model includes uncertainty in the exchange rate, weekly demand, and amounts of extra weekly capacity available. The future exchange rates are based on fitting historical exchange rates with @RISK's Time Series Fit tool.
