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基于引入宏观经济变量的仿射利率期限结构模型,本文构建了适合中国国情的提前还款模型。研究表明,国内住房抵押贷款的提前还款主要来自于收入和支付能力的提高。根据两个模型考虑了单因素和双因素两种情况,计算出相应的单月提前还款率(SMM)。在模型中考虑了异质性因素,加入了交易成本因素,并假设其服从beta分布,通过概率的变换得到SMM。在此基础上,在不同路径上模拟未来利率,利用提前还款模型对每条路径上的SMM进行计算,得到未来各期的现金流在某时点的折现值,而后对多条路径上的价格求算术平均值作为考虑提前还款后的住房抵押贷款理论价格。
Based on the term structure of affine interest rate with macroeconomic variables, this paper constructs an early repayment model that suits China’s national conditions. Research shows that the prepayment of domestic mortgage loans mainly comes from the increase of income and payment ability. According to the two models, one-factor and two-factor are considered, and the corresponding one-month early repayment rate (SMM) is calculated. We consider the heterogeneity factor in the model, add the transaction cost factor, and assume that it follows the beta distribution and get the SMM through the transformation of probability. Based on this, we simulate the future interest rates on different paths and use the prepayment model to calculate SMM on each path to get the discounted value of cash flow at a certain point in future periods. Then, The arithmetic mean of the price is taken as the theoretical price of a home mortgage loan after considering the prepayment.