Monte Carlo Simulation
In its most basic form, the Monte Carlo simulation seeks to simulate real-world outcomes by showing a range of outcomes for a given variable set. For example, in the casino game roulette, Monte Carlo could simulate where the roulette ball lands for 10 consecutive rounds.
Excel's "RAND" function can generate random numbers in a given sample set. By simply setting the formula equal to RAND, Excel will generate a random number between 0 and 1. To detail the range of possible outcomes, Microsoft states that around 25% of the time, a number less than or equal to 0.25 should occur, and around 20% of the time the number will be at least 0.90, which is logical and intuitive, given the outcomes are restricted to such a tight range.
Excel offers a number of other ways to simulate random variable outcomes. For instance, the "NORMINV" function returns the inverse of the normal distribution for a specified mean and standard deviation.
The valuation of stock options can be incredibly complex and math-intensive. Excel offers a number of ways to price stock options, including the more plain vanilla puts and calls. The Black-Scholes formula is the most widely adopted measure for valuing an option. Its inputs are as follows:
S=Today's stock price
t=Duration of the option (in years)
r=Annual risk-free rate (This rate is assumed to be continuously compounded.)
σ=Annual volatility of stock
y=Percentage of stock value paid annually in dividends
Excel doesn't have an actual formula employing Black-Scholes, but there are add-ins, as well as additional outside files that can be downloaded to help the user calculate the value of a put or call option.
Time Value of Money
The time value of money generally relates to the concepts of present value and future value, as explained previously in the PV Functions and FV Functions. The basic forms of the time value of money, which consists of multiplying an initial present value by an interest rate to get to a future value, can easily be calculated via a single cell calculation in Excel.
The more complicated theories, including DCF, DDM and RIM, require more sophisticated modeling techniques in Excel and have also been touched upon in previous pages.
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