Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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COMPARISON OF NUMERICAL SCHEMES ON MULTI-DIMENSIONAL BLACK-SCHOLES EQUATIONS

  • Jo, Joonglee (Department of Financial Engineering Ajou University) ;
  • Kim, Yongsik (Department of Financial Engineering Ajou University)
  • Received : 2012.12.19
  • Published : 2013.11.30
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Abstract

In this paper, we study numerical schemes for solving multi-dimensional option pricing problem. We compare the direct solving method and the Operator Splitting Method(OSM) by using finite difference approximations. By varying parameters of the Black-Scholes equations for the maximum on the call option problem, we observed that there is no significant difference between the two methods on the convergence criterion except a huge difference in computation cost. Therefore, the two methods are compatible in practice and one can improve the time efficiency by combining the OSM with parallel computation technique. We show numerical examples including the Equity-Linked Security(ELS) pricing based on either two assets or three assets by using the OSM with the Monte-Carlo Simulation as the benchmark.

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References

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Cited by

  1. A numerical study of RBFs-DQ method for multi-asset option pricing problems vol.36, pp.1, 2018, https://doi.org/10.5269/bspm.v36i1.29641
  2. On the multidimensional Black–Scholes partial differential equation pp.1572-9338, 2018, https://doi.org/10.1007/s10479-018-3001-1