2001/10/24 by Belal E. Baaquie
Economics, Econometrics and Finance · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Quantum Mechanics and Applications #Stochastic processes and financial applications #cond-mat.soft #cond-mat.stat-mech #q-fin.PR
paper · pdf · doi:10.1103/physreve.65.056122
7 Figures
arxiv created 2001/10/24 · openalex publication_date 2002/05/20 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.