Journal of the Korean Society for Industrial and Applied Mathematics

  • 제18권1호
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  • Pages.61-74
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  • 2014
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  • 1226-9433(pISSN)
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  • 1229-0645(eISSN)
한국산업응용수학회 (Korean Society for Industrial and Applied Mathematics)
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ACCURATE AND EFFICIENT COMPUTATIONS FOR THE GREEKS OF EUROPEAN MULTI-ASSET OPTIONS

  • Lee, Seunggyu (DEPARTMENT OF MATHEMATICS, KOREA UNIVERSITY) ;
  • Li, Yibao (DEPARTMENT OF COMPUTATIONAL SCIENCE AND ENGINEERING, YONSEI UNIVERSITY) ;
  • Choi, Yongho (DEPARTMENT OF MATHEMATICS, KOREA UNIVERSITY) ;
  • Hwang, Hyoungseok (DEPARTMENT OF FINANCIAL ENGINEERING, KOREA UNIVERSITY) ;
  • Kim, Junseok (DEPARTMENT OF MATHEMATICS, KOREA UNIVERSITY)
  • 투고 : 2014.02.06
  • 심사 : 2014.02.25
  • 발행 : 2014.03.25
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초록

This paper presents accurate and efficient numerical methods for calculating the sensitivities of two-asset European options, the Greeks. The Greeks are important financial instruments in management of economic value at risk due to changing market conditions. The option pricing model is based on the Black-Scholes partial differential equation. The model is discretized by using a finite difference method and resulting discrete equations are solved by means of an operator splitting method. For Delta, Gamma, and Theta, we investigate the effect of high-order discretizations. For Rho and Vega, we develop an accurate and robust automatic algorithm for finding an optimal value. A cash-or-nothing option is taken to demonstrate the performance of the proposed algorithm for calculating the Greeks. The results show that the new treatment gives automatic and robust calculations for the Greeks.

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참고문헌

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피인용 문헌

  1. A FAST AND ROBUST NUMERICAL METHOD FOR OPTION PRICES AND GREEKS IN A JUMP-DIFFUSION MODEL vol.22, pp.2, 2014, https://doi.org/10.7468/jksmeb.2015.22.2.159
  2. FINITE DIFFERENCE METHOD FOR THE TWO-DIMENSIONAL BLACK-SCHOLES EQUATION WITH A HYBRID BOUNDARY CONDITION vol.23, pp.1, 2014, https://doi.org/10.12941/jksiam.2019.23.019