TY - JOUR
T1 - On an efficient multiple time step Monte Carlo simulation of the SABR model
AU - Leitao, Álvaro
AU - Grzelak, Lech A.
AU - Oosterlee, Cornelis W.
PY - 2017
Y1 - 2017
N2 - In this paper, we will present a multiple time step Monte Carlo simulation technique for pricing options under the Stochastic Alpha Beta Rho model. The proposed method is an extension of the one time step Monte Carlo method that we proposed in an accompanying paper Leitao et al. [Appl. Math. Comput. 2017, 293, 461–479], for pricing European options in the context of the model calibration. A highly efficient method results, with many very interesting and nontrivial components, like Fourier inversion for the sum of log-normals, stochastic collocation, Gumbel copula, correlation approximation, that are not yet seen in combination within a Monte Carlo simulation. The present multiple time step Monte Carlo method is especially useful for long-term options and for exotic options.
AB - In this paper, we will present a multiple time step Monte Carlo simulation technique for pricing options under the Stochastic Alpha Beta Rho model. The proposed method is an extension of the one time step Monte Carlo method that we proposed in an accompanying paper Leitao et al. [Appl. Math. Comput. 2017, 293, 461–479], for pricing European options in the context of the model calibration. A highly efficient method results, with many very interesting and nontrivial components, like Fourier inversion for the sum of log-normals, stochastic collocation, Gumbel copula, correlation approximation, that are not yet seen in combination within a Monte Carlo simulation. The present multiple time step Monte Carlo method is especially useful for long-term options and for exotic options.
KW - Copulas
KW - Exact simulation
KW - Exotic options
KW - Fourier techniques
KW - Monte Carlo methods
KW - SABR model
KW - Stochastic collocation
UR - http://www.scopus.com/inward/record.url?scp=85017251108&partnerID=8YFLogxK
UR - http://resolver.tudelft.nl/uuid:d2555175-98ac-46fc-acdb-7549cd3a2851
U2 - 10.1080/14697688.2017.1301676
DO - 10.1080/14697688.2017.1301676
M3 - Article
AN - SCOPUS:85017251108
SN - 1469-7688
VL - 17
SP - 1549
EP - 1565
JO - Quantitative Finance
JF - Quantitative Finance
IS - 10
ER -