Supershares -- 3 state problem

[drsingh]

I am able to solve 3-state problem and their variations easily, like SOA sample question #27. Compute probabilities of each state (setup 3 equations, etc.)

But the below question from a mock test I am not able to follow. I don't understand how to go from prob to supershares.

Q: At the end of 6 months, 3 possible values of a market index. Super shares pay $1 at 6 months, if the associated price occurs, nothing otherwise. Index delta = 0.04, r=0.15.

Supershare Price Index price
Supershare 1 SS1 100
Supershare 2 SS2 135
Supershare 3 SS3 175

(a) 6 months cash or nothing put with payment trigger 120 is priced at 0.25
(b) 6 month asset or nothing call with payment trigger 125 is priced at 104.61.

My approach: Let p1, p2 and p3 be probabilities of each state.
First: p1+p2+p3=1
Second, cash put ==> 0.25= (1) p1 * exp(-.15*.5)
Third, asset call ==> 104.61 = (135 p2 + 175 p3) exp (-.15*.5)

From this I get p1, p2 and p3. Then what do I do to determine SS1, SS2 and SS3?

Can someone explain what a supershare really is? There's only a small side box in DM book, the only material I have used, and that is not very clear.

Thanks!

[Joe F]

A supershare pays $1 if and only if its associated state occurs. Therefore, using risk-neutral probabilities, we have:
SS1 = p1 * exp(-0.075)
SS2 = p2 * exp(-0.075)
SS3 = p3 * exp(-0.075)

The answer to the question is:
(2p1 - p2 + p3) * exp(-0.075)

[drsingh]

Thanks, got it. I also had a typos in the above, which I corrected.