Hi.I do an internship about pricing var swaps and I need to find a lower bound for the fair value (fair strike so-called Kvar) of var swap.Article Ref: http://www.ederman.com/new/docs/gs-vola ... waps.pdfOn page 20, you have the expression of Kvar:where S*=S0 (limit between OTM Puts and Calls for replication portofolio).My aim is to find a lower bound of function f (payoff). To begin, choose the part ST>S*. The lower bound will be a linear combination of calls with strikes Ki>S* (i>=1)My procedure: 1/ Step 1: Take the first call K1. I search the tangent at function f which passes by the point (K1;0). The point of tangence is called (x1;f(x1)) : it's easy to find it by using the Newton method and a study of function (no pbm for this step).2/ Step 2: I take all strikes between K1 and x1. Suppose for the example that only K2 is located before x1. My constraint for finding a lower bound is to undervalue the difference f(x1)- [ a1.max(x1-K1;0) + a2.max(x1-K2;0) ] where a1 and a2 are the weights of calls K1 and K2. In fact I want that the lower bound tries "to touch" the lof payoff f(ST), that's why I have introduced the tangent...I you generalize this equation, you obtain:If xi is the X-coordinate of the tangent at f passsing by strike Ki, the problem is to minimize the amount f(xi)-sum on j[ aj.max(xi-Kj;0) ] and to find the optimal set of {aj} (at less one...).Matric form: inf on X ||Y-AX|| where Y={f(xi)}, A={max(xi-Kj;0)} (A-matrix dim: i x j) and X={aj}.But I don't know how to find an optimal set of {aj}. Anyone can help me? Thanks a lot.

Apparently, you did not finish your question. Anyway, concerning lower bounds for variance swaps, you should have a look at "Robust replication of volatility derivatives", by Carr and Lee, who show that the ATMIV is a lower bound for the vol swap rate. Dupire also derived lower bounds for variance claims 'notably for a call on variance), see "Model free results on volaitlity derivatives".

sorry. my topic is complete now. thanks.

That was fast.

I read these articles but nothing for my pbm...