An IMEX‐BDF2 compact scheme for pricing options under regime‐switching jump‐diffusion models

Abstract

In this paper, an implicit‐explicit two‐step backward differentiation formula (IMEX‐BDF2) together with finite difference compact scheme is developed for the numerical pricing of European and American options whose asset price dynamics follow the regime‐switching jump‐diffusion process. It is shown that IMEX‐BDF2 method for solving this system of coupled partial integro‐differential equations is stable with the second‐order accuracy in time. On the basis of IMEX‐BDF2 time semi‐discrete method, we derive a fourth‐order compact (FOC) finite difference scheme for spatial discretization. Since the payoff function of the option at the strike price is not differentiable, the results show only second‐order accuracy in space. To remedy this, a local mesh refinement strategy is used near the strike price so that the accuracy achieves fourth order. Numerical results illustrate the effectiveness of the proposed method for European and American options under regime‐switching jump‐diffusion models.

Local Refinement and Adaptive Strategy for a System of Free Boundary Power Options with High Order Compact Differencing

“…For a description, please see Figure 1. For a similar implementation for solving the options pricing problem with a high-order compact scheme, please see the work of Chen et al [18] and Lee and Sun [19]. For the near boundary scheme, i.e, x 1 , we will consider fourth-order combined compact finite difference schemes for approximating the solution of the option value as given below…”

Numerical approach for coupled systems resulting from pricing of derivatives: Modeling and pricing of installment options

“…In the last decades, concerning the dynamic of risky assets, a number of alternative models have appeared in the finance literature to overcome the deficiencies in the standard geometric Brownian motion model that is known as the Black-Scholes-Merton model 16,17 ). In this respect, Regime switching (RS) models, 18,19 in which the dynamics of the change of economic regimes are modeled by a Markov chain, produce better results in fitting market data because they explain the jump patterns exhibited by some financial assets and have the potential to capture a wide variety of implied volatility skews in real markets. However, they are more difficult to handle compared with the basic Black-Scholes model.…”