Which of the following statements about options is false?

• The price of the option is less volatile than the price of the underlying stock
• option prices are generally higher the longer the time till the option expires
• for call options, the lower the strike price relative to the stock underlying price, the more the call option is worth
• prior to expiration, an expiration, an american option (call or put) may have higher value than an equivalent european option.
• for put options, the higher the strike price relative to the stocks underlying prices, the more the put is worth