does anyone know of a distribution for a random variable X which is non-negative, has 4 parameters to control its shape/moments, and for which the mgf is known in closed form?Also, anyone much experience with generalized lambda distNs?thx,M

for the SABR modeldS=S y dW1dy=y alpha dW2dW1dW2=0,does anyone know how to prove that S is a martingale + whether S is U.I.?The pth moment of S_T is infinite for p>1, + any T>0thx

http://users.iems.northwestern.edu/~linetsky/cev.pdfand Karatzas&Shreve

<t>isn't this related to Andersen+Piterbarg's work on Moment explosions?e.g. under an uncorrelated local-stoc vol modelwhere is the eigenfunction associated with the local vol component, so the highest moment of the exponential integrated variance that is finite is governed by the highest eigenfunct...

sorry, 1/d_x = E(sigma_T^2 | S_T=K= S0 exp(-x) =Dupire effective local voland Implied vol I(K) = x/d(x,y)

<t>in PC's toy modeldX=y dW_1dY= dW_2the relevant geodesic equation isy^2 d_x^2+ d_y^2 =1subject to d(x=0, y)=0d>=0where d_x is be the Dupire 96 effective local vol (x=lnS/K). Don't know off top of my head what the solution to this is, but under Hestonthe smile certainly isn't flat in short -maturit...

<t>sorry, I mean a contract paying sin S_T at T, which u could further decompose into Europeansusing the result that a general European payoff can be replicated with an infinite strip of OTM calls and puts, which is discussed inCM98 "Towards a theory of volatility trading" m is the speed measure =2/...

<t>u could think about spectral static hedging:e.g. Suppose we have stock price which follows standard Brownian motion starting at W_0 0<W_0<Pi, and we have a double knock out (DKO) call with terminal payoff sin(W_T), which also knocks out at x=0 or x=Pi. Then the price of the contract at time t<T i...

thx Alan; I've got the Lukacs book here if anyone needs me to quote from it

<r>simplest way is to calibrate a mixture model where vol can go up or down to two different known levels, to ATMs, 25d and 10d flies, and solve for ProbUp and the 2 volsu could extend this to vol going to n different levels, + solve for the n-1 probabilities as the solution to a linear eq Ax=b if u...

sorry meant meanreversion> volofvol

<t>yeah, read the attached, there's a pole in the complex planeif u set meanreversion<volofvol, then S_T will have finite 2nd moment for all T; they give an exact formula for computing the explosion timewhich will be exactly one of the solutions where your log blows upThe highest moment that is fini...

<t>If u've got the stones for it, use the theory of Large deviations:for a time-homogenous local vol model, u could use the vskew idea in the short-maturity limit to derive the implied vol of e.g. a One-Touch barrier optionLet S_t=g(W_t) where g is contrived so that S hits the smile at Tthen Priceof...

<t>for a fader that pays(S_T-K)^{+} I_Twhere dS=S sigma(S,t) dt dI = H(S_T-B) dti.e. call payoff times #days spot spends above B<Kwe can derive a Dupire fwd eq under local vol framework:d (S_T-K)^{+} I_T = H(S_T-K) I_T dS_T + 1/2 dirac(S_T-K) dS_T^2 + (S_T-K)^{+} H(S_T-B) dTso dFader/dT= 1/2 K^2 sig...

Does anyone know what a "multiplicity two" spectrum is, if so, could they give an example?thx