On an efficient multiple time step Monte Carlo simulation of the SABR model

On an efficient multiple time step Monte Carlo simulation of the SABR model

Leitao Rodriguez, A. (TU Delft Numerical Analysis; Centrum Wiskunde & Informatica (CWI))
Grzelak, L.A. (TU Delft Numerical Analysis; ING)
Oosterlee, C.W. (TU Delft Numerical Analysis; Centrum Wiskunde & Informatica (CWI))

2017

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.

Copulas
Exact simulation
Exotic options
Fourier techniques
Monte Carlo methods
SABR model
Stochastic collocation

http://resolver.tudelft.nl/uuid:d2555175-98ac-46fc-acdb-7549cd3a2851

https://doi.org/10.1080/14697688.2017.1301676

1469-7688

Quantitative Finance, 17 (10), 1549-1565

Institutional Repository

journal article

© 2017 A. Leitao Rodriguez, L.A. Grzelak, C.W. Oosterlee