AN OPERATOR SPLITTING METHOD FOR PRICING THE ELS OPTIONAN OPERATOR SPLITTING METHOD FOR PRICING THE ELS OPTION
- Other Titles
- AN OPERATOR SPLITTING METHOD FOR PRICING THE ELS OPTION
- Authors
- 김준석; 위인숙; 정다래
- Issue Date
- 2010
- Publisher
- 한국산업응용수학회
- Keywords
- operator splitting method; finite difference method; Black-Scholes equation
- Citation
- Journal of the Korean Society for Industrial and Applied Mathematics, v.14, no.3, pp.175 - 187
- Indexed
- KCI
- Journal Title
- Journal of the Korean Society for Industrial and Applied Mathematics
- Volume
- 14
- Number
- 3
- Start Page
- 175
- End Page
- 187
- URI
- https://scholar.korea.ac.kr/handle/2021.sw.korea/117603
- ISSN
- 1226-9433
- 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.
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