The Monte Carlo Option Model was developed to compute the exact value of a particular option using Monte Carlo Methods, as termed by Stanislaw Ulam. Designed by Phelim Boyle, this model was implemented for the first time in the year 1977 for the purpose of option pricing, which was applied for calculating the value of European options. A few years after, the model was also applied for determining the the values of American options, the process of which was discovered by E. S. Schwartz and F. A. Longstaff.
WHEN TO USE
In mathematical finance, options with simple or normal features are valued through the straightforward Black-Scholes process. The Monte Carlo Option Model, however, is used to calculate the following types of options:
- Options that relate to various sources of uncertainty, and calculating their values with other models is difficult.
- Options that exist in the market but have very complicated features.
- Arbitrage-free valuation of a definite derivative that consists of a large number of dimensions.
As the model requires a great deal of time for each analysis, it is used in limited situations.
APPLICATIONS
As can be seen, Monte Carlo Methods are particularly useful in the valuation of options with multiple sources of uncertainty or with complicated features which would make them difficult to value through a straightforward Black-Scholes style computation. The technique is thus widely used in valuing Asian options and in real options analysis .
Conversely, however, if an analytical technique for valuing the option exists – or even a numeric technique, such as a (modified) pricing tree – Monte Carlo methods will usually be too slow to be competitive. They are, in a sense, a method of last resort.