Simulation of coupon bond European and barrier options in quantum finance

Coupon bond European and barrier options are studied in the framework of quantum finance. The prices of European and barrier options are analyzed by generating sample values of the forward interest rates f(t,x)f(t,x) using a two-dimensional Gaussian quantum field A(t,x)A(t,x). The strong correlations of forward interest rates are described by the stiff propagator of the quantum field A(t,x)A(t,x). Using the Cholesky decomposition, A(t,x)A(t,x) is expressed in terms of white noise. The simulation results for European coupon bond and barrier options are compared with approximate formulas, which are obtained as power series in the volatility of the forward interest rates. The simulation shows that the simulated price deviates from the approximate value for large volatilities. The numerical algorithm is flexible and can be used for pricing any kind of option. It is shown that the three-factor HJM model can be derived from the quantum finance formulation.