Please use this identifier to cite or link to this item: https://doi.org/10.1103/PhysRevE.65.056122
Title: Quantum field theory of forward rates with stochastic volatility
Authors: Baaquie, B.E. 
Issue Date: May-2002
Citation: Baaquie, B.E. (2002-05). Quantum field theory of forward rates with stochastic volatility. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 65 (5) : 056122/1-056122/14. ScholarBank@NUS Repository. https://doi.org/10.1103/PhysRevE.65.056122
Abstract: In a recent formulation of a quantum field theory of forward rates, the volatility of the forward rates was taken to be deterministic. The field theory of the forward rates is generalized to the case of stochastic volatility. Two cases are analyzed, first when volatility is taken to be a function of the forward rates, and second when volatility is taken to be an independent quantum field. Since volatility is a positive valued quantum field, the full theory turns out to be an interacting nonlinear quantum field theory in two dimensions. The state space and Hamiltonian for the interacting theory are obtained, and shown to have a nontrivial structure due to the manifold moving with a constant velocity. The no arbitrage condition is reformulated in terms of the Hamiltonian of the system, and then exactly solved for the nonlinear interacting case. © 2002 The American Physical Society.
Source Title: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
URI: http://scholarbank.nus.edu.sg/handle/10635/97677
ISSN: 15393755
DOI: 10.1103/PhysRevE.65.056122
Appears in Collections:Staff Publications

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