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Consistent variance curve models. (English) Zbl 1101.91031
The author considers variance swaps as liquid derivatives and derives conditions such that the joint market of stock price and variance swap prices is free of arbitrage. A general approach to model such market in an HJM-type framework is considered. Then the finite-dimensional Markovian representations of the fixed time-to-maturity forward variance swap curve are introduced, and consistency results for both the standard case and for variance curves with values in a Hilbert space are derived. It is assumed that the realized variance paid by a variance swap is the realized quadratic variation of the logarithm of the index price. It is also assumed that the stock price process is continuous. The starting point is to assume that variance swaps are liquidly traded for all maturities. The aim of this paper is to first model the variance swap prices and then find an associated stock price process with compatible dynamics. A few examples of variance curve functionals is given and completeness and hedging in such models is discussed.

##### MSC:
 91B28 Finance etc. (MSC2000) 91B26 Auctions, bargaining, bidding and selling, and other market models
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