Which strike $100 worth.

Many of you would assume that the call option price,

in this case, should be much higher than the call option price in this case.

After all, the probability of going up is much higher.

So remember the payoff of a call option will be $10.00 and $0 in each case.

But with probability 0.99, I'm going to get the $10.00 here, but

with probability 0.01, I am going to get $10.00 here.

So it looks like owning a call option here should be a lot more

valuable than owning a call option on stock XYZ, okay?

But, that is not the case.

If you believe the assumptions of the model, that there is no transactions cost

and that you can borrow and lend at the risk-free rate of R, and

that you can buy or short sell the stock, then our previous analysis shows us

That the true value of the derivative security depends only on R and u and d.

It does not depend on the true probability's p.

And in fact, if my calculations are correct,

in both cases the option is worth approximately $4.80.

So C0 equals $4.80 here, and

C0 equals $4.80 here.

Now, at this point, a lot of people get upset.

They go, there's no way this could be the case.

There's something wrong here.

The theory that we've developed is wrong, you're, you're doing something incorrect.

But in fact, nothing I've done is incorrect.

What I've said here is correct.

The fair price of the option in both cases is $4.80.

So what I want you to do now is to think about this for a while.

And ask yourself what's going on.

Why is the fair option price $4.80 in both cases.

And to think about this.

I'll return to this in a couple of modules' time, and

we'll discuss this again, and hopefully we'll, we'll clarify what's going on and

explain why this apparent contradiction actually is not a contradiction at all.