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Volatility Arbitrage


What objective functions can be used to create a diversified volatility arbitrage portfolio?
My 2 cents based on derivatives pricing experience, the volatility arbitrage trading includes:

(1) Call/Put Spread Arbitrage and Butterfly Arbitrage: option structure strategies based on the arbitrage opportunity implied from the implied volatility smile.
(2) Calendar Spread Arbitrage: construct option strategy with different maturities to arbitrage on the implied volatility surface from maturity axis.

Just note that in a liquid market, normally such opportunities don't exist, since these are quite basic pricing check for big bank market makers.

There are some strategies also that is not real arbitrage, but more a statistical arbitrage and quite popular for volatility/correlation trading. For example:

Dispersion trading: trading the volatility of an index versus its components, to bet on the correlation estimation. The strategy involves exotic product trading like Variance Swap. For example, buying the Variance Swap of S&P 500 index and selling the Variance Swaps of a major portion of underlying stocks. If the stocks' realized correlation is higher than expectation, the index Var Swap is under-priced and you will profit in the end.

(Please correct me or enrich if anyone has better ideas on this topic.)