Dec 8, 2011

Leveraged ETFs : Volatility Skew

There is very little research available on taking volatility skew from regular (liquid) ETF and producing skew for inverse / leveraged ETF. Another related problem is producing consistent volatility skews between ETFs with the same underlying but different leverage factors.

The only source that I know of is PhD thesis of Jian (Stanley) Zhang, "Path-Dependence Properties of Leveraged Exchange-Traded Funds: Compounding, Volatility and Option Pricing" available for download here. The author presents 3 approaches to the solution.
  1. Author calibrates observed liquid options prices to Heston model and computed options on leveraged ETFs using MC. 
  2. Second approach is to compute prices of options on leveraged ETF as linear combination of "regular" ETF options, a-la var swap from options prices.
  3. Non-parametric skew model that translates "regular" ETF skew into leveraged ETF skew.
While research is certainly groundbreaking, these approaches suffer from some shortcomings. The first two are not directly application to American options, while the third lacks theoretical justification.

In the following posts I would like to elaborate on Dr Zhang's nonparametric approach, as well as two parametric approached that I developed. 

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