If the SP runs to $1 then yes of course the options can rise to a value of 80c
Think of it this way; you are the holder of some options and wish to sell them. Would you sell them for 50c knowing that the person that buys them off you will instantly convert them and sell the shares for $1 and make instant profit off you? You could do that yourself?
No. The market will value them at an appropriate price that reflects what they're worth
You will obviously not be able to sell them for $1 for 2 reasons
1. They have a strike price of 20c - that is money that is needed to be forked out to convert and this will reduce the value of the option
2. It has a time expiry. The more time left, then the higher the option will be worth. It has the ability to hang around while the company develops giving a trader more time to make a decision
In saying this, I think if the SP is above 20c, then the time value of the option has little impacts (correct me if im wrong)
Similarly, if the SP were to run to $10, then the option will be worth somewhere in the $9s with zero doubt
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