Fixed Income Derivatives modeling is a triumph of Mathematical Finance, since all major institutions use the theory for pricing, hedging, and management risk, is by far the largest instrument class.
In this project, a LIBOR Market Model (LMM), also known as the BGM Model (Brace Gatarek Musiela Model), is established for forward rate dynamics modeling. Pricing formulas for options are derived based on Black’s formula. A Monte Carlo simulation framework is designed to generate the stochastic processes. Then a binomial tree and a trinomial tree are set up to numerically solve the system respectively. The model is calibrated to the U.S. market swaption volatilities.