High-order Gaussian RBF-FD methods for real estate index derivatives with stochastic volatility

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.