Consistent variance curve models
type: Item
instance of: scholarly article
title: Consistent variance curve models
zbMATH Open document ID: 1101.91031
author: Hans Buehler
published in: Finance and Stochastics
publication date: 2006-12-08T00:00:00Z
review text: 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.
reviewed by: Yuliya S. Mishura
Mathematics Subject Classification ID: 91B28
Mathematics Subject Classification ID: 91B26
zbMATH DE Number: 5079136
zbMATH Keywords: variance swaps
zbMATH Keywords: options on variance
zbMATH Keywords: market models
zbMATH Keywords: arbitrage-free term structure dynamics
zbMATH Keywords: Heath-Jarrow-Morton theory
zbMATH Keywords: consistent parameterizations
MaRDI profile type: Publication
full work available at URL: s00780-006-0008-2
OpenAlex ID: W2098038575
cites work: Interest rate dynamics and consistent forward rate curves
cites work: On the existence of finite-dimensional realizations for nonlinear forward rate models.
cites work: Expensive martingales
cites work: Transform Analysis and Asset Pricing for Affine Jump-diffusions
cites work: Consistency problems for Heath-Jarrow-Morton interest rate models
cites work: On the geometry of the term structure of interest rates
cites work: Stochastic finance. An introduction in discrete time
cites work: Q4509488
cites work: Stochastic implied volatility. A factor-based model.
cites work: Bond Pricing and the Term Structure of Interest Rates: A New Methodology for Contingent Claims Valuation
cites work: A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options
cites work: Stochastic Equations in Infinite Dimensions
cites work: Q4435813
cites work: Q4226355
cites work: A market model for stochastic implied volatility
DOI: 10.1007/S00780-006-0008-2
description: scientific article; zbMATH DE number 5079136