Fourier Space Time-Stepping for Option Pricing With Levy Models

2007 ◽  
Author(s):  
Kenneth R. Jackson ◽  
Sebastian Jaimungal ◽  
Vladimir Surkov
Keyword(s):  
Option Pricing ◽  
Space Time ◽  
Fourier Space ◽  
Time Stepping

Fourier space time-stepping for option pricing with Lévy models

2008 ◽  
Vol 12 (2) ◽  
pp. 1-29 ◽  
Author(s):  
Kenneth Jackson ◽  
Sebastian Jaimungal ◽  
Vladimir Surkov
Keyword(s):  
Option Pricing ◽  
Space Time ◽  
Fourier Space ◽  
Time Stepping

FOURIER SPACE TIME-STEPPING ALGORITHM FOR VALUING GUARANTEED MINIMUM WITHDRAWAL BENEFITS IN VARIABLE ANNUITIES UNDER REGIME-SWITCHING AND STOCHASTIC MORTALITY

2017 ◽  
Vol 48 (1) ◽  
pp. 139-169 ◽  
Author(s):  
Katja Ignatieva ◽  
Andrew Song ◽  
Jonathan Ziveyi
Keyword(s):  
Regime Switching ◽  
Numerical Experiments ◽  
Space Time ◽  
Model Parameters ◽  
Percentage Increase ◽  
Fourier Space ◽  
Stochastic Mortality ◽  
Time Stepping ◽  
Force Of Interest ◽  
Stochastic Mortality Model

AbstractThis paper introduces the Fourier Space Time-Stepping algorithm to the valuation of variable annuity (VA) contracts embedded with guaranteed minimum withdrawal benefit (GMWB) riders when the underlying fund dynamics evolve under the influence of a regime-switching model. Mortality risk is introduced to the valuation framework by incorporating a two-factor affine stochastic mortality model proposed in Blackburn and Sherris (2013). The paper considers both, static and dynamic policyholder withdrawal behaviour associated with GMWB riders and assesses how model parameters influence the fees levied on providing such guarantees. Our numerical experiments reveal that the GMWB fees are very sensitive to regime-switching parameters; a percentage increase in the force of interest results in significant decrease in guarantee fees. The guarantee fees increase substantially with increasing volatility levels. Numerical experiments also highlight an increasing importance of mortality as maturity of the VA contract increases. Mortality has less impact on shorter maturity contracts regardless of the policyholder's withdrawal behaviour. As much as mortality influences pricing results for long maturities, the associated guarantee fees are decreasing functions of maturities for the VA contracts. Robustness checks of the Fourier Space Time-Stepping algorithm are performed by making numerical comparisons with several existing valuation approaches.

scholarly journals Explicit Time Stepping of PDEs with Local Refinement in Space-Time

2019 ◽  
Vol 81 (3) ◽  
pp. 1945-1962
Author(s):  
Dylan Abrahamsen ◽  
Bengt Fornberg
Keyword(s):  
Space Time ◽  
Local Refinement ◽  
Time Stepping
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