Crooked Volatility Smiles: Evidence from Leveraged and Inverse ETF Options
Published in the Journal of Derivatives & Hedge Funds 19, 278-294 (November 2013).
We find that leverage in exchange traded funds (ETFs) can affect the "crookedness" of
volatility smiles. This observation is consistent with the intuition that return shocks are
inversely correlated with volatility shocks - resulting in more expensive out-of-the-money
put options and less expensive out-of-the-money call options. We show that the prices of
options on leveraged and inverse ETFs can be used to better calibrate models of stochastic
volatility. In particular, we study a sextet of leveraged and inverse ETFs based on the S&P
500 index. We show that the Heston model (Heston , 1993) can reproduce the crooked smiles
observed in the market price of options on leveraged and inverse leveraged ETFs. We show
further that the model predicts a leverage dependent moneyness, consistent with empirical
data, at which options on positively and negatively leveraged ETFs have the same price.
Finally, by analyzing the asymptotic behavior for the implied variances at extreme strikes,
we observe an approximate symmetry between pairs of LETF smiles empirically consistent with the predictions of the Heston model.
The Rise and Fall of Apple-linked Structured Products
The rise in Apple's market capitalization in 2012 coincided with a dramatic increase in single-observation reverse convertibles, reverse convertibles and autocallable notes linked to Apple's stock price. These notes all transfer the downside risk of owning Apple to investors but cap the upside at somewhat more than corporate bond yields. Issuers use individual stocks like Apple as the reference obligations for reverse convertible structured products because investors underestimate the risk of suffering losses when the individual stock's price falls.
The decline in Apple's stock price from over $700 in September 2012 to $450 in January 2013 has resulted in over one hundred million dollars of losses in Apple-linked structured products. In this paper, we summarize our published reports on over 650 Apple-linked structured products and identify the impact of Apple's recent stock price decline on investors in these structured products.