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mcbison
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Posts: 199
Joined: January 18th, 2010, 9:26 am

vega in term of gamma

December 17th, 2010, 1:36 pm

what does it mean that vega is the integral of the gamma profits over the duration of the option at one volatility minus the same integral at a different volatility?
Last edited by mcbison on December 16th, 2010, 11:00 pm, edited 1 time in total.
 
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prodiptag
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Joined: September 12th, 2008, 4:41 pm

vega in term of gamma

December 22nd, 2010, 10:38 am

perhaps nothing much: in a black-schole world the pnl due to difference in price vol and realized vol can be expressed as gamma profits integrated over the option maturity at realized vol minus the same at price vol (see the paper "which free lunch would you like today, sir?: delta hedging, volatility arbitrage and optimal portfolios" by Ahmad and Wilmott for the exact expressions). this is equivalent to vega in some sense (and without normalizing i.e. vega in this sense is not dV/dVol, rather only dV due to change in vol)
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