Lever Options: Gamma Decay & Smiles
Levered ETFs are fascinating financial instruments. Derivatives on levered ETFs, termed lever options here (or, levers for shorthand), are even more interesting. As lever options are likely to be the first exotic to gain substantial exchange-traded volume, volatility traders should be salivating!
One of the most interesting aspects of levers is gamma decay (liberally inventing terminology, borrowing from the classic greek gamma):
Gamma decay is the decay in option value due to the leverage decay of the underlying levered instrument.
In other words, leverage decay in the underlying results in a direct effect on the derivative captured by gamma decay. Gamma decay is a non-trivial departure from the standard BSM assumption of a Weiner process underlying. Note gamma decay differs, although is similarly derived, from the linear scaling of the drift and volatility.
Most fundamentally, gamma decay should cause pause to evaluate the classic BSM gamma-theta tradeoff, now that both gamma and theta decay: .
Quick scan of the smiles for August expiry SSO and UPRO indicate MMs may still be pricing using classic BSM. Multi-order polynomial smile for SSO (fitted in blue, unfitted in gray), assuming 1.24% cont yield and 0% risk-free:
Similar smile for UPRO, assuming 0% cont yield and risk-free:
Subsequent posts will continue analysis of levers given they are such a rich vein.