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Analysis of variance based instruments for Ornstein–Uhlenbeck type models: swap and price index

Aziz Issaka () and Indranil SenGupta ()
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Aziz Issaka: North Dakota State University
Indranil SenGupta: North Dakota State University

Annals of Finance, 2017, vol. 13, issue 4, 401-434

Abstract: Abstract In this paper a couple of variance dependent instruments in the financial market are studied. Firstly, a number of aspects of the variance swap in connection to the Barndorff-Nielsen and Shephard model are studied. A partial integro-differential equation that describes the dynamics of the arbitrage-free price of the variance swap is formulated. Under appropriate assumptions for the first four cumulants of the driving subordinator, a Večeř-type theorem is proved. The bounds of the arbitrage-free variance swap price are also found. Finally, a price-weighted index modulated by market variance is introduced. The large-basket limit dynamics of the price index and the “error term” are derived. Empirical data driven numerical examples are provided in support of the proposed price index.

Keywords: Barndorff-Nielsen and Shephard model; Variance swap; Stochastic volatility; Price index; Weak convergence (search for similar items in EconPapers)
JEL-codes: C02 D53 G10 L16 (search for similar items in EconPapers)
Date: 2017
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