| TEACHING NOTE 96-03: (2004) | |||||||||||||
Abstract | |||||||||||||
| Simulation is a procedure in which random numbers are generated according to probabilities assumed to be associated with a source of uncertainty, such as a new product’s sales or, more appropriately for our purposes, stock prices, interest rates, exchange rates or commodity prices. Outcomes associated with these random drawings are then analyzed to determine the likely results and the associated risk. Oftentimes this technique is called Monte Carlo simulation, being named for the city of Monte Carlo, which is noted for its casinos. The gambling analogy notwithstanding, Monte Carlo simulation is a legitimate and widely used technique for dealing with uncertainty in many aspects of business operations. For our purposes, it has been shown to be an accurate method of pricing options and particularly useful for path-dependent options and others for which no known formula exists. To facilitate an understanding of the technique, we shall look at how Monte Carlo simulation has been used to price standard European options. Of course, we know that the Black-Scholes model is the correct method of pricing these options so Monte Carlo simulation is not really needed. It is useful, however, to conduct this experiment because it demonstrates the accuracy of the technique for a simple option of which the exact price is easily obtained from a known formula. The assumptions of the Black-Scholes model imply that for a given stock price at time t, simulated changes in the stock price at a future time t +)t can be generated by the following formula: | |||||||||||||
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