High-order Gaussian RBF-FD methods for real estate index derivatives with stochastic volatility. (January 2023) - Narsoo, Jason; Thakoor, Nawdha; Tangman, Yannick Désiré; Bhuruth, Muddun
Abstract: The 2008 financial crisis showed the necessity for managing risk associated with the price movements of real estate assets. Appropriate financial instruments for hedging real estate portfolios include options on a real estate index. Based on empirical evidence that real estate returns exhibit time varying volatility, a real estate index derivative pricing model with stochastic volatility is proposed. An efficient procedure using Gaussian radial basis functions-finite differences is developed for the numerical solution of the two-dimensional pricing partial differential equation. Fourth-order convergence rates on uniform meshes for European options are numerically demonstrated and the algorithm is also shown to compute accurate American option prices. A numerical study of the stability of the scheme reveals that errors remain small. Highlights: A one-factor real estate index model is augmented with stochastic volatility. The two-dimensional option pricing equation under the new model is derived. The Gaussian RBF-FD method is developed for the numerical valuation of options. The 5-point method is shown to compute accurate European and American option prices. Stability of the five-point scheme is numerically investigated.