Numerical solutions of PDEs for corporate bond pricing: A computational finance approach

Abstract. In this paper, we will see how one can use numerical algorithms to solve PDEs, containing partial derivative terms, for corporate bond pricing. We utilise the Black-Scholes framework which involves adding stochastic interest rates and credit risk into a PDE model. Then, we will take a quick look at some different numerical methods to solve the PDE model, like finite difference methods (FDM), finite element methods (FEM) as well as standard Monte Carlo (MC) simulations. Above all, we provide some simulations to show how well they work for PDEs, and how much time it takes. We would like to highlight that numerical methods lead to more accurate and efficient bond pricing with these methods, and also that we can analyse together how well each method works under different market scenarios. The paper will end with future directions for numerical methods, which should allow including more sophisticated algorithms and machine-learning techniques that improve scalability and can be used in a real-time manner in financial markets.