Fred Lande’s heart was pounding as he watched Tesla Inc. shares charge to an all-time high of $968.99 last week. It wasn’t because he was happy.

He’d bet thousands of dollars that the frantic rally that has more than tripled the price of the shares in just a few months was doomed to end, and soon. Concluding his gamble was wrong, he closed the options trade at a loss.

“Someone...