In this paper, we consider the COS method for pricing European and Bermudan options under the stochastic alpha beta rho (SABR) model. In the COS pricing method, we make use of the characteristic function of the discrete forward process. We observe second-order convergence by using a second-order Taylor scheme in the discretization, or by using Richardson extrapolation in combination with a Euler–Maruyama discretization on the forward process. We also consider backward stochastic differential equations under the SABR model, using the discretized forward process and Fourier-cosine expansion for the occurring expectations. For this purpose, we extend the so-called BCOS method from one to two dimensions.

Additional Metadata
Keywords backward stochastic differential equation, COS method, Euler–Maruyama scheme, Richardson extrapolation, SABR
Persistent URL dx.doi.org/10.1080/00207160.2017.1290438
Journal International Journal of Computer Mathematics
Citation
van der Have, Z, & Oosterlee, C.W. (2017). The COS method for option valuation under the SABR dynamics. International Journal of Computer Mathematics, 1–21. doi:10.1080/00207160.2017.1290438