I am doing Exercise 1.13 in Introduction to Mathematical Finance: Discrete Time Models by Pliska.
Exercise 1.13 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 both are marketable or neither is marketable. Use risk neutral evaluation to show that the former case one has $$c-p=S_0-e/(1+r).$$
The parity at last is reached by book-keeping calculation. However, I don't know how to show the simultaneous marketability of call/put option with same exercise price. Could anyone hint me? Thanks in advance!
Here, marketable means: There exists some trading strategy $H$ such that $H$ generates $X$, i.e., the $t=1$ value of portfolio $V_1=X$.