ASM 6th Exam#8 question 10

[Kurt Lee]

The problem asks for the probability that an option modeled with a binomial tree will have value at expiry. We are given both the risk free rate, and the annnual rate of return on the stock.

Why do we use true probabilities to solve?

[Abraham Weishaus]

Because that's what the problem asks for.

[Kurt Lee]

If we were asked to calculate the value of the option, we would want to use the risk free rate, but because we are calculating the probability that the option "will have value" at expiry, we are really valuing the stock at expiry. So it implicitly asks for the true probability, where as in exam seven, number thirteen asks directly for the risk neutral probability of a payoff for an option.

Is this what you mean by the problem asking for it?

[Abraham Weishaus]

Yes. Probability is true probability unless you're told otherwise. The word "true" is added only to distinguish it from the risk-neutral probability when both are given.