Pricing the Financial Heston Model Using Parallel Finite Difference Method on GPU CUDA

Abstract

An option is a financial instrument in which two parties agree to exchange assets at a price or strike and the date or maturity is predetermined. Options can provide investors with information to set strategies so they can increase profits and reduce risk. Option prices need to be accurately evaluated according to reality and quickly so that the resulting value can be utilized at the best momentum. Valuation of option prices can use the Heston equation model which has advantages compared to other equation models because the assumption of volatility is not constant with time or stochastic volatility. The volatility that is not constant with time corresponds to reality because the underlying asset as a basis can experience fluctuations. The Heston equation has a disadvantage because it is a derivative equation that is difficult to solve. One way to solve derivative equations easily is to use a numerical solution to the finite difference method of non-uniform grids because the Heston equation can be assumed to be a parabolic equation. The numerical solution of the finite difference method can solve derivative equations flexibly and do not require matrix processing. But it requires a heavy and slow computing process because there are many elements of calculation and iteration. This study proposes a numerical solution to the finite difference method by using the Compute Unified Device Architecture (CUDA) parallel programming to solve the Heston equation model that applies the concept of stochastic volatility to get accurate and fast results. The results of this research proved 15.52 times faster in conducting parallel computing processes with error of 0.0016..