Portfolio Insurance

[anubis]

Hello everbody

I hope i'm at the right place with my question

We have to do a homework in finance, an one question is the following:

"Assume an insured portfolio containing a long position in the risk-free asset and a long position in call options. The risky postition contains call options on share Y. All options expire in one year. Share Y is traded at 150 CHF and has a volotility of 30% per annum.
Based on C1 with N(z1)= 0.95, what is the probability that the insured portfolio will participate at the performance of share Y?"

Thank you very much for your answer.

 

[David Harper CFA FRM]

I'm thrown by the nonstandard C1/zi, but if N(d1) = 0.95 ...
N(d2) is the risk-neutral probability that option will be exercised and d2 = d1 - volatility *SQRT(T)
so N(d1) = 0.95 implies d1 = 1.645, such that d2 = 1.645 - 30% vol *SQRT(1 year) = 1.345
N(d2) = N(1.345) = 91.07% .... but don't quote me b/c i am not sure i followed the question

David

 

[anubis]

I think you followed the question. Thank you very much.

 

[anubis]

oh, iguess its not the right answer, because its not in a risk-neutral world.

What about N((d1+d2)/2) ?

 

[David Harper CFA FRM]

Right, N(d2) under BSM is the risk-neutral prob of ITM/exercise (assuming riskfree rate enters...can't tell). I don't know about N((d1+d2)/2) but, again, I am unclear on C1 and whether N(z1) = N(d1) ... i personally can't find answer from stated question, I perceive missing information. Sorry, David

 

[anubis]

C1 means call number one (because in the question there are three possible calls) and N(z1) = N(d1).
I don't know either about N((d1+d2)/2) .