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MODEL‐INDEPENDENT LOWER BOUND ON VARIANCE SWAPS
Author(s) -
Kahalé Nabil
Publication year - 2016
Publication title -
mathematical finance
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.98
H-Index - 81
eISSN - 1467-9965
pISSN - 0960-1627
DOI - 10.1111/mafi.12083
Subject(s) - variance swap , infimum and supremum , variance risk premium , variance (accounting) , econometrics , portfolio , realized variance , mathematics , upper and lower bounds , economics , maturity (psychological) , stochastic game , volatility (finance) , mathematical economics , price variance , stochastic volatility , implied volatility , financial economics , volatility swap , combinatorics , mathematical analysis , developmental psychology , psychology , accounting , volatility risk premium
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.