Model-Independent Lower Bound on Variance Swaps

Abstract:     
It is well known that, under a continuity assumption on the price of a stock S, the realized variance on S for maturity T can be replicated by a portfolio of calls and puts maturing at T. This paper assumes call prices on S maturing at T are known for all strikes but makes no continuity assumptions on S. We derive semi-explicit expressions for the supremum lower bound Vinf on the hedged payoff, at maturity T, of a long position n the realized variance of S. Equivalently, Vinf is the supremum strike K such that an investor with a long position in a variance swap with strike K can ensure to have a non-negative payoff at T. We study examples with constant implied volatilities and with a volatility skew. In our examples, Vinf is rather close to the fair variance strike obtained under the continuity assumption.

Number of Pages in PDF File: 21

Keywords: model risk, hedging, sub-replication, realized variance, variance swap

JEL Classification: G10, G13

working papers series