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

Darae Jeong, Minhyun Yoo, Junseok Kim

Research output: Contribution to journalArticle

2 Citations (Scopus)

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.

Original languageEnglish
Article number1586786
JournalDiscrete Dynamics in Nature and Society
Volume2016
DOIs
Publication statusPublished - 2016

Fingerprint

Black-Scholes Equation
Finite difference method
Partial differential equations
Numerical methods
Black-Scholes
Truncation Error
Time Stepping
Test Problems
Difference Method
Tolerance
Finite Difference
Partial differential equation
Numerical Methods
Numerical Solution
Calculate
Numerical Results
Computing

ASJC Scopus subject areas

  • Modelling and Simulation

Cite this

Accurate and Efficient Computations of the Greeks for Options Near Expiry Using the Black-Scholes Equations. / Jeong, Darae; Yoo, Minhyun; Kim, Junseok.

In: Discrete Dynamics in Nature and Society, Vol. 2016, 1586786, 2016.

Research output: Contribution to journalArticle

@article{0b969a95ae5a48ae84f8ca6075bceb89,
title = "Accurate and Efficient Computations of the Greeks for Options Near Expiry Using the Black-Scholes Equations",
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.",
author = "Darae Jeong and Minhyun Yoo and Junseok Kim",
year = "2016",
doi = "10.1155/2016/1586786",
language = "English",
volume = "2016",
journal = "Discrete Dynamics in Nature and Society",
issn = "1026-0226",
publisher = "Hindawi Publishing Corporation",

}

TY - JOUR

T1 - Accurate and Efficient Computations of the Greeks for Options Near Expiry Using the Black-Scholes Equations

AU - Jeong, Darae

AU - Yoo, Minhyun

AU - Kim, Junseok

PY - 2016

Y1 - 2016

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84965160657&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84965160657&partnerID=8YFLogxK

U2 - 10.1155/2016/1586786

DO - 10.1155/2016/1586786

M3 - Article

AN - SCOPUS:84965160657

VL - 2016

JO - Discrete Dynamics in Nature and Society

JF - Discrete Dynamics in Nature and Society

SN - 1026-0226

M1 - 1586786

ER -