Implicit-explicit Runge-Kutta methods for pricing financial derivatives in state-dependent regime-switching jump-diffusion models (Q6584729)

The authors of the article propose a numerical method for pricing financial derivative instruments. The model they consider is based on jump-diffusion model with the regime switching. They assume that an economy can be in one of \(H\) possible regimes at any given time and that regime switching can be described as a Markov chain. In each regime the price of a stock dynamic, \(S_t\), is governed by a jump-diffusion model:\N\[\N\frac{dS_t}{S_{t-}} = \mu^i_t dt + \sigma^i_t dW_t + dN^i_t\N\]\Nwhere \(W\) is a Wiener process and \(N^i\) is are compound Poisson processes representing jumps. The drift \(\mu^i\), the volatility \(\sigma^i\) and the jump process \(N^i\) depend on the current regime \(i\).\N\NIn this setup the authors consider the pricing of a derivative instrument with a general payoff function \(h(s)\). The instrument may be of European or American type. The value function in both cases is a solution of a partial integro-differential equation or a partial integro-differential inequality. The authors present a method for solving this problem numerically using the implicit-explicit Runge-Kutta method. For American instruments, the authors use the operator splitting technique combined with implicit-explicit methods.\N\NThe main theoretical results are Theorems 1 and 2, which prove the consistency and convergence in \(l_2\) norm of the proposed methods. The authors give explicit algorithms for pricing, based on the proposed methods and provides numerical examples of calculations.