Question

If I sell a PUT option contract, the most that I can lose is the exercise price of the stock, and that only if the stock goes to zero. (Never happens),

But, as we discussed, if I sell a CALL option, then the potential (at least theoretic) loss is unlimited, infinite if the stock goes to the moon.

So, why would anyone in their right might write call options?

Answer 1

While its known that call writer has unlimited exposure of loss. But still they write calls. There are various reason discussed below -

1) To hedge the equity position : call writer may want to hedge the equity position (Long in equity). so he may sell call in such case he is limited to some extent its losses due to fall in price, and at the same time his call loss is recovered if price increases from existing equity position.

2) to speculate : Some trader do the speculation and they sale call. They are typically high networth individual or big investor banker.

3) Arbitrage opportunity - Lots of financial strategies are their to make arbitrage profit (risk less profit) using buying and selling of financial instrument, these include staddle, staple , Butterfly etc.. They involve sell of call option as well but they do simultaneously buying selling of options, future etc..