I ask merely about pairs of Bear (Inverse) and Bull (Leveraged) ETFs for the same underlying index. The Bear ETF's price shall be bounded below by 0. But the bull ETF's price is unbounded.
But doesn't this difference — in boundedness — cause an dissymmetry in pricing options on Bear and Bull ETFs? On one hand, they shall be priced the same. Why? Any difference shall be arbitraged away, because you can buy the pricier options on one direction, and sell the cheaper options on the other direction.
On the other hand, the return on the Bear ETF is bounded below by 0. As the bear ETF's price nears 0, its put option shall near its absolute maximum (strike price — option premium). But the bull ETF's price — and its option price — are UNbounded above!
Example With YINN (Daily FTSE China Bull 3X Shares) And YANG (Daily FTSE China Bear 3X Shares).
If the underlying FTSE China 50 Index rallies, then YINN can skyrocket unbounded, so can call options on YINN. But YANG must minimize at 0, so must put options on YANG.
The asymmetry is that YINN call option's price is unbounded. But YANG put option's price shall be bounded and maximized, when YANG's price = 0.
Conversely, if the underlying FTSE China 50 Index crashes, then YINN shall minimize at 0, so can put options on YINN. But YANG can skyrocket unbounded, so can call options on YANG!
The asymmetry is that YANG call option's price is unbounded. But YINN put option's price shall be bounded and maximized, when YINN's price = 0.