유한차분법과 병렬 시뮬레이션을 통한 주택저당증권 가치 평가

Abstract

In this paper, we apply parallel computing using a message-passing interface to pricing the Mortgage Backed Securities (MBS) with multiple tranches. We use the Finite Difference Method (FDM) to the differential equations of modeling MBS and determine the numerical solutions for the MBS. Our benchmark is the MBS 2017-11 issued by the Korean Housing Corporation. To obtain the interest rate condition for mortgage early repayment under the CIR (Cox et al., 1985) assumption, we calibrate the key variables on the interest rate process by the General Method of Moment (GMM). We also define the boundary conditions of the solutions in risk-neutral valuation through the Monte Carlo simulations. Our results suggest that the MBS needs to be issued with a long maturity to keep the risk-neutral position. Finally, we show that the parallel computing process successfully reduces costs and time for MBS pricing.