The COS method for option valuation under the SABR dynamics

In this paper,we consider theCOSmethod for pricing European andBermudan 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. ARTICLE HISTORY Received 24 February 2016 Revised 22 June 2016 Accepted 28 September 2016