In: Statistics and Probability
1) Monte Carlo Simulation
The Monte Carlo method is a stochastic (random sampling of inputs) method to solve a statistical problem, and a simulation is a virtual representation of a problem. The Monte Carlo simulation combines the two to give us a powerful tool that allows us to obtain a distribution (array) of results for any statistical problem with numerous inputs sampled over and over again. The Monte Carlo simulation has numerous applications in finance and other fields. Monte Carlo is used in corporate finance to model components of project cash flow, which are impacted by uncertainty. The result is a range of net present values (NPVs) along with observations on the average NPV of the investment under analysis and its volatility. The investor can, thus, estimate the probability that NPV will be greater than zero. Monte Carlo is used for option pricing where numerous random paths for the price of an underlying asset are generated, each having an associated payoff. These payoffs are then discounted back to the present and averaged to get the option price. It is similarly used for pricing fixed incomesecurities and interest rate derivatives. But the Monte Carlo simulation is used most extensively in portfolio management and personal financial planning
2) Discounted cash flow modeling
A typical discounted cashflow model for a potential investment makes forecasts of costs and revenues over the life of the project and discounts those revenues back to a present value. Most analysts start with a 'base case' model and add uncertainty to the important elements of the model.