Accurate and Efficient Computations of the Greeks for Options Near Expiry Using the Black-Scholes Equations
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 disc...
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| Format: | Article |
| Language: | English |
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Wiley
2016-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2016/1586786 |
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| _version_ | 1850164121575620608 |
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| author | Darae Jeong Minhyun Yoo Junseok Kim |
| author_facet | Darae Jeong Minhyun Yoo Junseok Kim |
| author_sort | Darae Jeong |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-eb283bfad1aa4601ad9e4e29836e3557 |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2016-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-eb283bfad1aa4601ad9e4e29836e35572025-08-20T02:22:03ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2016-01-01201610.1155/2016/15867861586786Accurate and Efficient Computations of the Greeks for Options Near Expiry Using the Black-Scholes EquationsDarae Jeong0Minhyun Yoo1Junseok Kim2Department of Mathematics, Korea University, Seoul 136-713, Republic of KoreaDepartment of Financial Engineering, Korea University, Seoul 136-701, Republic of KoreaDepartment of Mathematics, Korea University, Seoul 136-713, Republic of KoreaWe 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.http://dx.doi.org/10.1155/2016/1586786 |
| spellingShingle | Darae Jeong Minhyun Yoo Junseok Kim Accurate and Efficient Computations of the Greeks for Options Near Expiry Using the Black-Scholes Equations Discrete Dynamics in Nature and Society |
| title | Accurate and Efficient Computations of the Greeks for Options Near Expiry Using the Black-Scholes Equations |
| title_full | Accurate and Efficient Computations of the Greeks for Options Near Expiry Using the Black-Scholes Equations |
| title_fullStr | Accurate and Efficient Computations of the Greeks for Options Near Expiry Using the Black-Scholes Equations |
| title_full_unstemmed | Accurate and Efficient Computations of the Greeks for Options Near Expiry Using the Black-Scholes Equations |
| title_short | Accurate and Efficient Computations of the Greeks for Options Near Expiry Using the Black-Scholes Equations |
| title_sort | accurate and efficient computations of the greeks for options near expiry using the black scholes equations |
| url | http://dx.doi.org/10.1155/2016/1586786 |
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