Which Free Lunch Would You Like Today, Sir?: Delta Hedging, Volatility Arbitrage and Optimal Portfolios

Riaz Ahmad and Paul Wilmott examine the statistical properties of the profit to be made from hedging vanilla options that are mispriced by the market and/or hedged using a delta based on different volatilities. Formulas for the expected profit and the variance of profit for single options and for portfolios of options on the same underlying are derived and several ways to choose optimal portfolios are suggested

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