Scanning through schweser, I came across this
As a final example of risk-neutral pricing and replication, consider an investor who buys a share of stock, sells a call on the stock at 40, and buys a put on the stock at 40 with the same expiration date as the call. The investor will receive 40 at option expiration regardless of the stock price because:
If the stock price is 40 at expiration, the put and the call are both worthless atexpiration.
If the stock price > 40 at expiration, the call will be exercised, the stock will be delivered for 40, and the put will expire worthless.
If the stock price is < 40 at expiration, the put will be exercised, the stock will be delivered for 40, and the call will expire worthless.
Thus, for a six-month call and put we can write:
stock + put - call = 40/(1+R)0.5 and equivalently
call stock + put-40/(1+Rf)0.5 and put = call +40/(1+Rf)0.5 - stock
It says consider an investor who buys a put and sells a call, which implies a short call and means we’d benefit from a drop in price. If stock price is less than <40, our strike price, I understand why the put gets delivered, but why would the call option expire worthless? The same’s my query for the second point where our investor is benefiting from S>X while holding a short call…or am I missing something?