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MULTI‐ASSET STOCHASTIC LOCAL VARIANCE CONTRACTS
Author(s) -
Carr Peter,
Laurence Peter
Publication year - 2011
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/j.1467-9965.2010.00422.x
Subject(s) - variance swap , variance (accounting) , stochastic game , asset (computer security) , econometrics , economics , futures contract , generalization , financial economics , hedge , stock (firearms) , variance risk premium , asset allocation , mathematical economics , mathematics , stochastic volatility , volatility swap , computer science , volatility (finance) , portfolio , implied volatility , computer security , volatility risk premium , mathematical analysis , ecology , engineering , biology , accounting , mechanical engineering
Variance swaps now trade actively over‐the‐counter (OTC) on both stocks and stock indices. Also trading OTC are variations on variance swaps which localize the payoff in time, in the underlying asset price, or both. Given that the price of the underlying asset evolves continuously over time, it is well known that there exists a semirobust hedge for these localized variance contracts. Remarkably, the hedge succeeds even though the stochastic process describing the instantaneous variance is never specified. In this paper, we present a generalization of these results to the case of two or more underlying assets.