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Accurate and Efficient Computations of the Greeks for Options Near Expiry Using the Black-Scholes Equations

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  • Darae Jeong
  • Minhyun Yoo
  • Junseok Kim

Abstract

We investigate the accurate computations for the Greeks using the numerical solutions of the Black-Scholes partial differential equation. In particular, we study the behaviors of the Greeks close to the maturity time and in the neighborhood around the strike price. The Black-Scholes equation is discretized using a nonuniform finite difference method. We propose a new adaptive time-stepping algorithm based on local truncation error. As a test problem for our numerical method, we consider a European cash-or-nothing call option. To show the effect of the adaptive stepping strategy, we calculate option price and its Greeks with various tolerances. Several numerical results confirm that the proposed method is fast, accurate, and practical in computing option price and the Greeks.

Suggested Citation

  • Darae Jeong & Minhyun Yoo & Junseok Kim, 2016. "Accurate and Efficient Computations of the Greeks for Options Near Expiry Using the Black-Scholes Equations," Discrete Dynamics in Nature and Society, Hindawi, vol. 2016, pages 1-12, April.
    • Handle: RePEc:hin:jnddns:1586786
    DOI: 10.1155/2016/1586786
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    References listed on IDEAS

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    1. A. Golbabai & L. Ballestra & D. Ahmadian, 2014. "A Highly Accurate Finite Element Method to Price Discrete Double Barrier Options," Computational Economics, Springer;Society for Computational Economics, vol. 44(2), pages 153-173, August.
    2. Zvan, R. & Vetzal, K. R. & Forsyth, P. A., 2000. "PDE methods for pricing barrier options," Journal of Economic Dynamics and Control, Elsevier, vol. 24(11-12), pages 1563-1590, October.
    3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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