Vega and Theta bleeding

paolopiace · April 5th, 2012, 12:11 am

Assume a generic delta neutral options position on one underlying and one expiration.Today the position has value V and carries a certain Theta and Vega.I expect that tomorrow the ATM iVol will drop N percent points.Therefore, excluding other effects, by tomorrow V will drop by the amount of Theta -N x Vega.Question:being delta neutral today, how can I calculate the amount the underlying must move for compensating the bleeding caused by Theta and -N x Vega?Thanks!

Alan · April 7th, 2012, 1:57 pm

I would ignore theta, so if V(S0,sigimplied0) is the value of your position today, just solve forS1 in V(S1,sigimplied1) = V(S0,sigimplied0)

paolopiace · April 7th, 2012, 3:50 pm

Thank you!Actually, I ended up using Gamma, since (dS)^2 ~ (sigma S)^2 dtKnowing the one day PnL = Theta -N x Vega0.5 Gamma (dS)^2 =PnL gives dS= sqrt( 2 PnL / Gamma )That should be the average movement of the underlying that compensates PnL in a Delta hedged position.Yet, I would appreciate comments, if any, on that.