November 19th, 2009, 2:22 pm
Hi,For short-dated variance swaps, if the expected realized variance is calculated continuously.the fair strike for the variance swap is given by EQ27 of the Demeterfi-Derman-Kamal-Zou paper.PI_cp is the present value of the portfolio of continuous infinitely close options with payoff at expiry given by f(S_T)That portfolio, in appendix A, is approximated with a set of discrete options with weights calculated so that thelinear approximation exceeds slightly the convex curve. Obviously, by tending the number of options to infinity, andthe range to [0, infinity[, we reach the theoretical fair strike for the swap. The linear approximation becomes an =My question is small and technical. Once we calculated the price of the portfolio of the discrete options, do weforward that price with exp(rT)?ie, is the linear approximation for PI_cp or for exp(rT)*PI_cp?that is, do we need to multiply 419.8671 * exp(rT) ?rds,