Consistent Variance Curve Models

Authors: Hans Buehler

Publish Date: 2006/04/26

Volume: 10, Issue: 2, Pages: 178-

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Abstract

We introduce a general approach to model a joint market of stock price and a term structure of variance swaps in an HJMtype framework In such a model strongly volatilitydependent contracts can be priced and riskmanaged in terms of the observed stock and variance swap prices To this end we introduce equity forward variance term structure models and derive the respective HJMtype arbitrage conditions We then discuss finitedimensional Markovian representations of the fixed timetomaturity forward variance swap curve and derive consistency results for both the standard case and for variance curves with values in a Hilbert space For the latter our representation also ensures nonnegativity of the process We then give a few examples of such variance curve functionals and briefly discuss completeness and hedging in such models As a further application we show that the speed of mean reversion in some standard stochastic volatility models should be kept constant when the model is recalibrated

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