Publication:
Simulation of nonlinear interest rates in quantum finance: Libor Market Model
Abstract
The simulation of the Libor Market Model (LMM) is extensively studied in the frame work of quantum finance.The imperfectly correlated Libor rates are simulated based on a Gaussian quantum field and a recursion equation of nontrivial stochastic drift. The Libor options are studied using both the simulation method and the analytical formula. The caplet price of simulation is compared with Black's caplet formula which can be exactly derived from the LMM. The invariance of caplet price for different forward bond numeraire is verified by using the simulation. The simulation results for coupon bond options and swaptions are compared with the approximate price, which are limited for the reason that the approximate price is derived using the small volatility expansion. The simulation method is shown to have great potential in the application of pricing interest rate instruments.
Keywords
Quantum finance , Libor Market Model , Coupon bond options , Caplet , Swaptions , Monte Carlo simulation
Citation
Baaquie, B. E., & Pan, T. (2012). Simulation of nonlinear interest rates in quantum finance: Libor Market Model. Physica A, 391(4), 1287-1308. https://doi.org/10.1016/j.physa.2011.08.021
Publisher
Elsevier