Hi everyone

This is my first time in these forums and was wondering if anyone could help me with this question?

I enrolled in some finance subjects, and this particular subject happens to be heavily mathematical, and I am having quite some problems, as I do not have a maths background...

I am required to derive a proof on reset strike options.

CR(S) = Price of Reset Call Option with inital stock price St and reset price Sr. Payoff = Max{St-min(Sr,K),0}

PR(S) = Price of Reset Put Option with inital stock price St and reset price Sr. Payoff = Max{max(Sr,K)-St,0}

C(S) = Price of Vanilla Call Option with inital stock price St

P(S) = Price of Vanilla Put Option with inital stock price St

S is stock price

K is strike price

t is option maturity

r is strike reset date

a) Prove that CR(S) >= C(S) and PR(S) >= P(S), for all values S.

b) For what values of r do the inequalities above become equalities?

I have been struggling with this for quite some time and any help would be greatly appreciated.

Thanks in advance!