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Abstract

This paper presents the numerical valuation of the two-asset step-down equitylinked securities (ELS) option by using the operator-splitting method (OSM). The ELS is one of the most popular financial options. The value of ELS option can be modeled by a modified Black-Scholes partial differential equation. However, regardless of whether there is a closedform solution, it is difficult and not efficient to evaluate the solution because such a solution would be represented by multiple integrations. Thus, a fast and accurate numerical algorithm is needed to value the price of the ELS option. This paper uses a finite difference method to discretize the governing equation and applies the OSM to solve the resulting discrete equations. The OSM is very robust and accurate in evaluating finite difference discretizations. We provide a detailed numerical algorithm and computational results showing the performance of the method for two underlying asset option pricing problems such as cash-or-nothing and stepdown ELS. Final option value of two-asset step-down ELS is obtained by a weighted average value using probability which is estimated by performing a MC simulation.

참고문헌 (14)

  1. Y. Achdou and O. Pironneau, Computational methods for option pricing, SIAM, Philadelphia, 2005. 
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  3. D.J. Duffy, Finite difference methods in financial engineering : a partial differential equation approach, John Wiley and Sons, New York, 2006. 
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  10. R. Seydel, Tools for computational finance, Springer Verlag, Berlin, 2003. 
  11. D. Tavella and C. Randall, Pricing financial instruments:the finite difference method, John Wiley and Sons, New York, 2000. 
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  14. R. Zvan, K. R. Vetzal and P.A. Forsyth, PDE methods for pricing barrier options, Journal of Economic Dynamics and Control, 24 (2000), 1563-1590. 

이 논문을 인용한 문헌 (1)

  1. Jeong, Darae, Li, Yibao, Choi, Yongho, Moon, Kyoung-Sook, Kim, Junseok 2013. "AN ADAPTIVE MULTIGRID TECHNIQUE FOR OPTION PRICING UNDER THE BLACK-SCHOLES MODEL" Journal of the Korean Society for Industrial and Applied Mathematics, 17(4): 295~306 

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