FAST AND EFFICIENT NUMERICAL METHOD FOR THE PENALTY TSIVERIOTIS-FERNANDES MODEL

FAST AND EFFICIENT NUMERICAL METHOD FOR THE PENALTY TSIVERIOTIS-FERNANDES MODEL

Conventional approaches to valuing convertible bonds typically evaluate early exercise conditions sequentially, which can be computationally intensive, particularly for bonds with both callable and puttable features. To improve efficiency, this paper proposes a fast and efficient numerical method for solving the penalty Tsiveriotis-Fernandes (TF) model, which is widely used for pricing convertible bonds. By incorporating a piecewise-uniform mesh and newly developed algorithms for the efficient application of early exercise conditions, the proposed approach significantly reduces computational costs while preserving high accuracy. By using a piecewise-uniform mesh to reduce the total number of condition evaluations, the proposed algorithms further reduce the number of evaluations by first determining the stopping indices for early exercise conditions on both sides of the optimal point, and then applying Newton's iteration, combined with the finite difference method (FDM), within a restricted range based on the left index. Through numerical experiments on two representative examples, the method is shown to deliver at least an eightfold improvement in computational speed compared to conventional uniform FDM, without compromising numerical precision. Our proposed approach results in improved efficiency, particularly for convertible bond pricing applications that require immediate execution.