This question is from Pliska's "Introduction to Mathematical Finance"
Suppose the interest rate r is a scalar, and let c and p denote the prices of a call and put, respectively, both having the same exercise price e. Show that either are marketable or neither is marketable. Use the risk neutral valuation to show that in the former case one has c-p=S_{0}-e/(1+r).
I am not really sure how to get started on this problem. Any help is greatly appreciated.
I know that for it to be marketable is that same as it being attainable.
I remember that book. I hated it with passion. Anyways, for the formula when both are marketable:
Let $T$ denote the end date and $B_t$ the bank account. If they are marketable there will be a risk-neutral measure $\mathbb Q$ such that $$ c = E^{\mathbb Q}((S_T -e)^+/B_T) $$ and $$ p = E^{\mathbb Q}((e-S_T)^+/B_T) $$ So $$ c-p = E^{\mathbb Q}\left(\frac{(S_T -e)^+-(e-S_T)^+}{B_T} \right) = E^{\mathbb Q}\left(\frac{S_T -e}{B_T} \right) = E^{\mathbb Q}\left(\frac{S_T}{B_T} \right)-E^{\mathbb Q}\left(\frac{e}{B_T} \right)\\=S_0-\frac{e}{1+r} $$