Numerically pricing convertible bonds under stochastic volatility or stochastic interest rate with an ADI-based predictor-corrector scheme

Abstract In this paper, the pricing problem for the American-style convertible bonds with the Heston stochastic volatility and that with the Cox–Ingersoll–Ross (CIR) stochastic interest rate are both considered. Due to the complexity of both problems, resulting from an additional stochastic factor, it is almost impossible to find any analytical solution. Therefore, a predictor–corrector scheme is chosen as the numerical scheme to solve the partial differential equations (PDEs), with the Douglas–Rachford (D–R) method being utilized as one of the Alternating Direction Implicit (ADI) methods for the correction step to obtain the numerical solution. Finally, the accuracy of our approach is numerically verified, and different properties of convertible bond price and the optimal conversion price are also demonstrated and discussed through examples.

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