TY - JOUR
T1 - The COS method for option valuation under the SABR dynamics
AU - van der Have, Z.
AU - Oosterlee, C. W.
PY - 2018
Y1 - 2018
N2 - 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.
AB - 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.
KW - backward stochastic differential equation
KW - COS method
KW - Euler–Maruyama scheme
KW - Richardson extrapolation
KW - SABR
UR - http://www.scopus.com/inward/record.url?scp=85014531019&partnerID=8YFLogxK
UR - http://resolver.tudelft.nl/uuid:32e958ad-613a-4f6f-8160-fd203a27d8c5
U2 - 10.1080/00207160.2017.1290438
DO - 10.1080/00207160.2017.1290438
M3 - Article
AN - SCOPUS:85014531019
SN - 0020-7160
VL - 95
SP - 444
EP - 464
JO - International Journal of Computer Mathematics
JF - International Journal of Computer Mathematics
IS - 2
ER -