Consistent Variance Curve Models

Hans Buehler ()
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Hans Buehler: Deutsche Bank AG London

Finance and Stochastics, 2006, vol. 10, issue 2, No 2, 178-203

Abstract: Abstract We introduce a general approach to model a joint market of stock price and a term structure of variance swaps in an HJM-type framework. In such a model, strongly volatility-dependent contracts can be priced and risk-managed 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 HJM-type arbitrage conditions. We then discuss finite-dimensional Markovian representations of the fixed time-to-maturity 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 non-negativity 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.

Keywords: Variance swaps; Options on variance; Market models; Arbitrage-free term structure dynamics; Heath–Jarrow–Morton theory; Consistent parametrizations; 91B24; G13 (search for similar items in EconPapers)
Date: 2006
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Citations: View citations in EconPapers (29)

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DOI: 10.1007/s00780-006-0008-2

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