Valuing Prepayment and Default in a Fixed‐Rate Mortgage: A Bivariate Binomial Options Pricing Technique
用双变量二项式期权定价法为固定利率抵押贷款中的提前还款和违约期权估值，发现与有限差分模型相比，期权价值差异在利率期限结构向下倾斜且调整缓慢时较大（超过贷款额的5%），在利率和房地产波动率低时较小（低于0.5%）。
This paper uses a bivariate binomial options pricing technique to value prepayment and default options in a fixed-rate mortgage. By forcing the two underlying state variables (real-estate value and spot rate of interest) to undergo transformations, a computationally simple bivariate binomial lattice is created. Compared with the finite-difference model of Kau et al. (1992, 1994), large option value differences (over 5% of the loan) are rare and occur when there is a downward-sloping term structure and slow adjustment. The smallest option value differences (less than 0.5% of the loan) tend to occur when interest-rate volatility and real estate volatility are low.