When you buy options you're buying exactly that, the option to make a potentially lucrative trade in the future at a price agreed now. (Bought) Puts have just as limited downside as (bought) calls.
The bigger risk comes in selling options: you sell a call and (assuming you don't already have the underlying shares) your downside is unlimited - you might have to pay sky high market prices only to sell (to the call option holder) low; you sell a put and your downside could be the entire strike price - the underlying could have gone to zero but you're forced to buy high (at the agreed price).
The bigger risk comes in selling options: you sell a call and (assuming you don't already have the underlying shares) your downside is unlimited - you might have to pay sky high market prices only to sell (to the call option holder) low; you sell a put and your downside could be the entire strike price - the underlying could have gone to zero but you're forced to buy high (at the agreed price).