Yes, you can use calculus/derivatives to value many financial derivatives. However, you can also use calculus to model how much water is in a bathtub that drain

Yes, you can use calculus/derivatives to value many financial derivatives. However, you can also use calculus to model how much water is in a bathtub that drains a different amount of water depending on how much water is in the bathtub. My point was that financial derivatives weren't named after math derivatives. Also, to elaborate, if you buy a call and sell a put, you will be betting precisely on the change in the price [of the underlying] because you have created a synthetic stock position (because of Put-Call parity: http://en.wikipedia.org/wiki/Put%E2%80%93call_parity http://en.wikipedia.org/wiki/Put%E2%80%93call_parity).