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Put versus call option prices

OK, please correct me if I am wrong, but a put option is when your stock is sold automatically when the price drops below a certain level.
a call is the option to purchase stock at a given price.

If you have the amount that a put option would cost - how would you figure out what a call option would cost?

3 month put option exercise price of $50 (trading in a narrow range) is $4
Risk free rate is 10%/year
how much is a 3 month call option?

Solution Preview

no, the stock is not sold automatically. you have to exercise the option to sell stock.
yes, call option is right (option) to ...