Abstract
We apply the radial basis function (RBF) collocation method to solve the
coupled system of partial di erential equations (PDEs), which arises in modelling
derivatives prices with regime-switching models. Spatial discretisation
is achieved through global RBF expansion. It converts the coupled system
of PDEs into a system of ordinary di erential equations (ODEs). The initial
and boundary conditions of the original coupled PDEs become the initial
conditions and algebraic constraints of the system of ODEs. Thus, our initial
problem is converted into a system of di erential-algebraic equations (DAEs).
This system of DAEs is solved using solvers available as libraries in Julia. Our
results compare favourably to those obtained using nite di erence method
and Monte Carlo simulation.
Keywords: Option pricing, Coupled Partial Di erential Equation, Regimeswitching
model, Radial basis functions, Black-Scholes, Markov chain.