MODEL‐INDEPENDENT LOWER BOUND ON VARIANCE SWAPS

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