MODEL‐INDEPENDENT LOWER BOUND ON VARIANCE SWAPS
在不假设股票价格连续的情况下，推导出方差互换多头在到期时能保证非负收益的最大执行价格，并用常数隐含波动率和波动率偏斜的例子验证该下界接近连续假设下的公平方差执行价。
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 on the hedged payoff, at maturity T , of a long position in the realized variance of S . Equivalently, 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, is close to the fair variance strike obtained under the continuity assumption.