#TITLE_ALTERNATIVE# - Hidayat (NIM 20204027), Arief
ABSTRACT: In 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, firstly when volatility is taken to be a function of forward rates, and secondly when volatility ia taken to be an independent quantum field. Since volatility is a positive quantum field, the full theory turns out to be an interacting non-liniear quantum field 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 constant velocity. The no arbitrage condition is reformulated in terms of the Hamiltoninan of the system, and then solved for the nonlinear interacting case.