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The price of an American option is given by $V_n = \max\{G_n, \frac{1}{1 + r}(pV_{n +1}(H) + qV_{n + 1}(T)\}$, where $p$, $q$ are the risk neutral probabilities.

I have two questions.

  1. How can one intuitively see that this must be the formula to avoid arbitrage? If possible cite a trivial example showing arbitrage if one does not take the maximum of these two values.

  2. How to intuitively see that the ideal time to exercise the option is $\min\{n: V_n = G_n\}$ ?

Thanks.

Michael Hardy
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user7348
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  • This is great source to get your answers http://www.springer.com/mathematics/quantitative+finance/book/978-0-387-40100-3 – Ehsan M. Kermani Aug 28 '14 at 03:09
  • An option on what? If it's a call option on a non-dividend paying stock then you never want to exercise early. It's also possible you might find more enlightening answers at the http://quant.stackexchange.com – Tyler Aug 28 '14 at 03:35

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