In this paper, a new approach, the Variance Gamma (VG) model, which is used to capture unexpected shocks (e.g., Covid-19) in housing markets, is proposed to contribute to the standard option-based mortgage valuation methods. Based on the VG model, the closed-form solutions are performed for pricing mortgage default and prepayment options. It solves the options pricing equations explicitly and illustrates numerical results for both mortgage default and prepayment options’ prices. Furthermore, the study enables researchers to monitor the default probability of mortgagors. Analyzing the effect of risks on default and prepayment options using simulations shows that the VG model captures the systematic and systemic (idiosyncratic) risks of default and prepayment options prices with closed-form solutions and computes the mortgage default probabilities. Therefore, it allows lenders a more advanced decision process compared to the standard option-based mortgage valuation method.

在本文中，提出了一种新方法，即方差伽玛 (VG) 模型，该模型用于捕捉住房市场中的意外冲击（例如 Covid-19），以促进基于标准期权的抵押贷款估值方法。基于 VG 模型，对抵押违约和提前还款选项进行定价的封闭形式解决方案。它明确地求解了期权定价方程，并说明了抵押贷款违约和提前还款期权价格的数值结果。此外，该研究使研究人员能够监控抵押人的违约概率。使用模拟分析风险对违约和提前还款期权的影响表明，VG 模型使用封闭式解决方案捕捉违约和提前还款期权价格的系统性和系统性（异质）风险，并计算抵押贷款违约概率。