# Why is a short call worthless, if price is less than exercise price?

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?

Why would the owner of the option exercise it when the market price is below the strike?

But didn’t an investor in this example sell a call? Yes, the owner or the long party of the call wouldn’t exercise, when the spot is lower than strike, but isn’t the call option not worthless to our investor who simultaneously bought a put option and sold a call?

The call wasn’t worthless when we sold it originally – we received a premium to sell it – but it’s worthless at expiry.

Okay, so it’s basically a shift to the long call position’s point of view when they describe the worthlessness of the option?

If that’s so, it’s a rather strangely put example. Or maybe I’m missing out on something silly-ly. Either ways, i do understand risk neutral pricing, so not getting this example won’t do much harm.