Sample Question #109 (finance – option pricing)

Imagine you’re asked to implement a Monte Carlo simulation of a stock option’s price. Is it better to simulate the option price itself, or simulate the stock price and then calculate the option price?

(Comment: this is a case-type question; remember the technique for handling such questions I advocate in my book?)

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ANSWER

There’s no right or wrong answer on this one, as long as you can give good justification to your answer.

In general, though, it’s easier to simulate the price movement of the underlying rather than the derivative. The reason is we can reasonably assume that the underlying’s price follows an easy-to-study distribution. For instance, stock prices closely follow a lognormal distribution. When you know the distribution, you can simulate it. Derivatives like options, on the other hand, have "irregular" distributions that we can’t capture adequately; for instance, there’re often strange kinks and then you need to worry about leverage and time decay. Just too complicated, don’t you think?