Let V be the value of a derivative written on an asset whose time t=o value is and whose value in the next period at time t=1 will be or , where and is the interest rate for the period. Suppose the derivative value in the next period is correspondingly and . Show by constructing an appropriate portfolio that
The background to this question is a chapter in Mathematics for Finance and Valuation entitled "One period, one risky asset and two states" where the risk-neutral probability was introduced and used to value the forward contract and call and put options.
I cannot get to that equation. My attempt at solution:
First, I find state probabilities (eg is the probability of "up" state and so on) from the current price of asset S:
Then I assume I can use the same probabilities to value the derivative claim on the asset S (can I?). The value of the derivative in one year's time V(1+r) should be
So my answer is different from the instruction by one component: I have and they have . Any comments?
Another question, does interest r=1 make sense?... Is that 100%?