ABSTRACT Real estate assets can be used to store capital, generate income through rentals and can act as collateral for debt instruments. Common risk management mechanisms for real estate investments use portfolio diversification techniques, but these techniques require large amounts of capital to work effectively. Real estate index derivatives offer an alternative mechanism for managing risks associated with real estate investments. They also increase market liquidity by providing a path for individuals who do not own real estate assets to participate in the real estate market. We consider the problem of pricing real estate index derivative contracts. The market is incomplete, so it is completed by futures derivatives on the same real estate index. A dynamic hedging strategy is employed leading to a parabolic partial differential equation with coefficients which are dependent on time and the real estate index. We then construct a nonstandard finite difference method to price European and American real estate index options. The scheme utilizes complete cubic spline interpolants of the option prices at time-dependent backtrack points on the spatial grid. Bounds for the global error are theoretically established. Numerical experiments are carried out to illustrate the accuracy of the scheme.

中文翻译：

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用于定价房地产指数期权的稳健非标准有限差分方案

摘要 房地产资产可用于储存资本、通过租金产生收入，并可作为债务工具的抵押品。房地产投资的常见风险管理机制使用投资组合多样化技术，但这些技术需要大量资金才能有效运作。房地产指数衍生品为管理与房地产投资相关的风险提供了一种替代机制。它们还通过为不拥有房地产资产的个人参与房地产市场提供途径来增加市场流动性。我们考虑房地产指数衍生合约的定价问题。市场是不完整的，所以它是由同一房地产指数的期货衍生品来完成的。采用动态对冲策略导致抛物线偏微分方程的系数取决于时间和房地产指数。然后我们构建了一个非标准的有限差分方法来为欧美房地产指数期权定价。该方案在空间网格上的时间相关回溯点使用期权价格的完整三次样条插值。理论上建立了全局误差的界限。进行了数值实验以说明该方案的准确性。该方案在空间网格上的时间相关回溯点使用期权价格的完整三次样条插值。理论上建立了全局误差的界限。进行了数值实验以说明该方案的准确性。该方案在空间网格上的时间相关回溯点使用期权价格的完整三次样条插值。理论上建立了全局误差的界限。进行了数值实验以说明该方案的准确性。