Asm 3.14 ?

[Hawgdriver]

I don't understand the answer to this problem. The option is worth the same for both volatilities according to the fact that expected future value of the stock at time T is strictly related to the risk free rate, and is unchanged by a change in volatility.

However, if you determine the premium based on the computed u1,d1 and u2,d2 -- you end up with different payouts with different corresponding probabilities.

I calculated the difference in premiums of the two alternate volatilities as the risk-free discounted value of (premium 1 X probability 1 - premium 2 X probability 2), and got a non-zero answer.

I guess I don't understand why the options are worth the same if the expected payout (So X u1 - K vs. So X u2 - K) for each option is different.

Thanks in advance for any help!

[Abraham Weishaus]

Not true - the higher the volatility, the more the option pays. Imagine if there were no volatility. The option would then be worth 5 discounted, and nothing more.

[Hawgdriver]

Dr. Weishaus,

So is the answer of 0 (change in option premiums when sigma varies from .2 to .3) that is in the exercise solutions for Lesson 3 then incorrect? If that is not the case, I'm afraid I still don't understand the solution. If it is the case, then what is the correct answer? I did not see errata for that solution, but I may have overlooked it. Thanks again for the help--and should I post on this forum or email the "mail@studymanuals.com"?

[Abraham Weishaus]

It's only correct because the option pays off regardless under both volatilities.