This paper examines how credit guarantees and government subsidies impact investment in a regime-switching model. We provide new explicit pricing formulas for a general standard asset. Almost all common corporate securities’ prices can be easily derived by the explicit formulas though project cash flows are driven by both a Brownian motion and a two-state Markov chain. We provide a method about how governments should specify a proper tax subsidy standard for a given tax rate to motivate a firm to invest in a project in the way they wish. If the tax subsidy is sufficiently high (low), an overinvestment (underinvestment) occurs. The higher the tax rate, the more significant the overinvestment (underinvestment). We pin down the subsidy amount required for motivating a firm to invest immediately and fix the optimal capital structure with government subsidies.

This paper investigates the volatility in regime-switching models formulated based on the geometric Brownian motion with its drift and volatility factors randomized with Markov chains. By developing explicit formulas about occupation time of Markov chains, we analysis the difference between global volatility of this model and the volatility caused by Brownian randomness, in order to measure the volatility caused by regime-switching after justifying its existence. Utilizing this structure of volatility, we optimize the methods of volatility parameters estimation.

A numerical comparison of the Monte Carlo (MC) simulation and the finite-difference method for pricing European options under a regime-switching framework is presented in this paper. We consider pricing options on stocks having two to four volatility regimes. Numerical results show that the MC simulation outperforms the Crank–Nicolson (CN) finite-difference method in both the low-frequency case and the high-frequency case. Even though both methods have linear growth, as the number of regimes increases, the computational time of CN grows much faster than that of MC. In addition, for the two-state case, we propose a much faster simulation algorithm whose computational time is almost independent of the switching frequency. We also investigate the performances of two variance-reduction techniques: antithetic variates and control variates, to further improve the efficiency of the simulation.