Pricing foreign exchange options under stochastic volatility and\n interest rates using an RBF--FD method

2019/03/03 by Fazlollah Soleymani, Andrey Itkin, Soleymani, Fazlollah +1
Economics, Econometrics and Finance · Mathematics · #Affine transformation #Algorithm #Applied mathematics #Artificial neural network #Computation #Computational Finance (q-fin.CP) #Computer science #Differential Equations and Numerical Methods #Econometrics #Economics #FOS: Economics and business #FOS: Mathematics #Finance #Financial economics #Greeks #Interest rate #Interest rate derivative #Mathematical analysis #Mathematical optimization #Mathematics #Numerical Analysis (math.NA) #Numerical analysis #Numerical methods for differential equations #Partial differential equation #Pricing of Securities (q-fin.PR) #Radial basis function #Stochastic differential equation #Stochastic processes and financial applications #Stochastic volatility #Valuation of options #Volatility (finance)

paper · pdf · doi:10.48550/arxiv.1903.00937

published in arXiv (Cornell University) (Cornell University)

openalex publication_date 2019/03/03 · openalex created_date 2022/07/29 · openalex updated_date 2026/07/28

Abstract

This paper proposes a numerical method for pricing foreign exchange (FX)\noptions in a model which deals with stochastic interest rates and stochastic\nvolatility of the FX rate. The model considers four stochastic drivers, each\nrepresented by an It ^o's diffusion with time--dependent drift, and with a\nfull matrix of correlations. It is known that prices of FX options in this\nmodel can be found by solving an associated backward partial differential\nequation (PDE). However, it contains non--affine terms, which makes its\ndifficult to solve it analytically. Also, a standard approach of solving it\nnumerically by using traditional finite--difference (FD) or finite elements\n(FE) methods suffers from the high computational burden. Therefore, in this\npaper a flavor of a localized radial basis functions (RBFs) method, RBF--FD, is\ndeveloped which allows for a good accuracy at a relatively low computational\ncost. Results of numerical simulations are presented which demonstrate\nefficiency of such an approach in terms of both performance and accuracy for\npricing FX options and computation of the associated Greeks.\n

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