scholarly journals Twisted K-theory constructions in the case of a decomposable Dixmier-Douady class

2014 ◽  
Vol 14 (2) ◽  
pp. 247-272 ◽  
Author(s):  
Antti J. Harju ◽  
Jouko Mickelsson
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Lie Groups ◽  
Explicit Construction ◽  
Theory Model ◽  
Quantum Field ◽  
Compact Lie Groups ◽  
Field Theory Model ◽  
Cup Product ◽  
K Theory

AbstractTwisted K-theory on a manifold X, with twisting in the 3rd integral cohomology, is discussed in the case when X is a product of a circle and a manifold M. The twist is assumed to be decomposable as a cup product of the basic integral one form on and an integral class in H2(M,ℤ). This case was studied some time ago by V. Mathai, R. Melrose, and I.M. Singer. Our aim is to give an explicit construction for the twisted K-theory classes using a quantum field theory model, in the same spirit as the supersymmetric Wess-Zumino-Witten model is used for constructing (equivariant) twisted K-theory classes on compact Lie groups.

scholarly journals A COMMON MARKET MEASURE FOR LIBOR AND PRICING CAPS, FLOORS AND SWAPS IN A FIELD THEORY OF FORWARD INTEREST RATES

2005 ◽  
Vol 08 (08) ◽  
pp. 999-1018 ◽  
Author(s):  
BELAL E. BAAQUIE
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Interest Rate ◽  
Interest Rates ◽  
General Class ◽  
Theory Model ◽  
Common Market ◽  
Quantum Field ◽  
Bond Price ◽  
Forward Measure

The main result of this paper is that a martingale evolution can be chosen for LIBOR such that, by appropriately fixing the drift, all LIBOR interest rates have a common market measure. LIBOR is described using a quantum field theory model, and a common measure is seen to emerge naturally for such models. To elaborate how the martingale for the LIBOR belongs to the general class of numeraires for the forward interest rates, two other numeraires are considered, namely the money market measure that makes the evolution of the zero coupon bonds a martingale, and the forward measure for which the forward bond price is a martingale. The price of an interest rate cap is computed for all three numeraires, and is shown to be numeraire invariant. Put-call parity is discussed in some detail and shown to emerge due to some nontrivial properties of the numeraires. Some properties of swaps, and their relation to caps and floors, are briefly discussed.

scholarly journals A Quantum Field Theory Term Structure Model Applied to Hedging

2003 ◽  
Vol 06 (05) ◽  
pp. 443-467 ◽  
Author(s):  
Belal E. Baaquie ◽  
Marakani Srikant ◽  
Mitch C. Warachka
Keyword(s):  
Field Theory ◽  
Quantum Field Theory ◽  
Term Structure ◽  
Theory Model ◽  
Forward Rate ◽  
Quantum Field ◽  
Structure Model ◽  
Term Structure Model ◽  
Forward Rates ◽  
Low Dimensional

A quantum field theory generalization, Baaquie [1], of the Heath, Jarrow and Morton (HJM) [10] term structure model parsimoniously describes the evolution of imperfectly correlated forward rates. Field theory also offers powerful computational tools to compute path integrals which naturally arise from all forward rate models. Specifically, incorporating field theory into the term structure facilitates hedge parameters that reduce to their finite factor HJM counterparts under special correlation structures. Although investors are unable to perfectly hedge against an infinite number of term structure perturbations in a field theory model, empirical evidence using market data reveals the effectiveness of a low dimensional hedge portfolio.

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