<t>You might want to check out the following paper: it contains all the formulae and symmetries between the various barrier type options, single, double (exponentially curved) barriers under geometric Brownian Motion.J.K.Hoogland and C.D.D.Neumann, Local scale invariance and contingent claim pricing...

<t>1)you fit the mixed densities to the current smileSo this fixes the set {p_i,\Sigma_i}, then you're doneAt the money by construction the implied vol will be constant for this set of fitted parameters.2)you then fit sigma(S,t) to the mixed densities?? the stuff has been fitted in step 1) So i don'...

why is this the case? I don't think it's true.well, it simply follows from the followingsum_i p_i BS(S,K P,Sigma_i) = BS(S,K P,Sigma_Implied(S,K P))ATM we have S=K P, hence, using homogeneitysum_i p_i BS(1,1,Sigma_i) = BS(1,1,Sigma_Implied(1,1))All dependance on the spot drops out...Jiri

<t>MJ, maybe i miss something in your argument.Let me give a counter example.Let's consider the following simple case, where I have a stock with normal dynamics.When I back out the implied vol, I get a smile, which moves in the same direction as the spot.So this is a simple local vol model, that doe...

<t>Does anybody have a proof of the claim that a local vol model is not able to have a sticky delta for the implied vol curve?In the SABR article Hagan etal show that for their approximation around the strike a local vol model doesn't capture the sticky delta behavior.Some years ago there was appear...

A European option with discrete dividend is an asian option in disguise.To value it you can use an Asian option formula. The details you can find in the following paper:Article: Asians and cash dividends: exploiting symmetries in pricing theoryJiri

<t>QuoteOriginally posted by: prosperoS(t)^p exp(-rt) is not a martingale, but S(t)^p exp( sigma^2 p(1-p)t/2 -prt ) is.Can't we take S(t)^p exp(sigma^2 p(1-p)t/2 +(1-p)rt) as numeraire? It seems that the rest follows as in the vanilla case, with the drift of S being adjusted according to this new me...

<r>You can find more info on the use of power tradables inhttp://<URL url="http://www.cwi.nl/~neumann/download/M9919.pdfhttp://www.cwi.nl/~neumann/download/jumpdif.pdfandhttp://www.cwi.nl/~neumann/download/gaussian.pdfWe"><LINK_TEXT text="www.cwi.nl/~neumann/download/M9919.pdfh ... sian.pdfWe">www.c...

<r>Maybe the following link provides some additional info:<URL url="http://www.cwi.nl/~neumann/download/jumpdif.pdfIt%27s">http://www.cwi.nl/~neumann/download/jumpdif.pdfIt's</URL> another angle on arriving at option prices than using martingales,maybe it adds some insight in changing measures and s...