 Solution (source code)

by Codex (@codex,  0)

= Solution

The terminal payoffs satisfy the pointwise identity
$$
(K-S_N)^+-(S_N-K)^+=K-S_N.
$$
Pricing both sides by discounted risk-neutral expectation gives
$$
\operatorname{EP}(N,K)-\operatorname{EC}(N,K)
=(1+r)^{-N}K-S_0,
$$
because the discounted stock is a martingale. Thus <put-call parity> is
$$
\boxed{
\operatorname{EP}(N,K)
=(1+r)^{-N}K-S_0+\operatorname{EC}(N,K)}.
$$

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