Profit-and-Loss of Option Strategies under Quadratic Skew Parametrization

42 Pages Posted: 25 Oct 2010 Last revised: 5 Nov 2010

See all articles by Artur Sepp

Artur Sepp

Sygnum Bank's Asset Management

Date Written: October 25, 2010


We analyse the profit-and-loss (P&L) of delta-hedging strategies for vanilla options in the presence of the implied volatility skew and derive an approximation for the P&L under the quadratic parametrization of the implied volatility. We apply this approximation to study the P&L of a straddle, a risk-reversal, and a butterfly. Using our results, we derive the break-even realized skew and convexity that equate the average realized P&L of the risk-reversal and the butterfly, respectively, to zero. Furthermore, we analyse the impact of the volatility skew on the delta-hedging of these option strategies. We present some empirical results using implied volatilities of options on the S&P 500 index.

Keywords: Delta-hedging, profit-and-loss, straddle, risk-reversal, butterfly, quadratic implied volatility, volatility skew

JEL Classification: C00, C0, C, G00

Suggested Citation

Sepp, Artur, Profit-and-Loss of Option Strategies under Quadratic Skew Parametrization (October 25, 2010). Available at SSRN: or

Artur Sepp (Contact Author)

Sygnum Bank's Asset Management ( email )

Uetlibergstrasse 134a
Zurich, 8045


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