High-order Gaussian RBF-FD methods for real estate index derivatives with stochastic volatility. (January 2023)

• Record Type: Journal Article
• Authors: Narsoo, Jason; Thakoor, Nawdha; Tangman, Yannick Désiré; Bhuruth, Muddun
• Is Part Of: Engineering analysis with boundary elements. Volume 146(2023)
• Page Start: 869
• Page End: 879
• Publication Date: 2023-01
• Subjects: Real estate index derivatives -- Stochastic volatility -- Gaussian RBF-FD -- American options; Boundary element methods -- Periodicals; Engineering mathematics -- Periodicals; Équations intégrales de frontière, Méthodes des -- Périodiques; Mathématiques de l'ingénieur -- Périodiques; Boundary element methods; Engineering mathematics; Periodicals; 620.00151
• DOI: 10.1016/j.enganabound.2022.11.015
• Languages: English
• ISSNs: 0955-7997

Abstract

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.