Accurate and efficient computations of the Greeks for options near expiry using the Black-Scholes equations
type: Item
instance of: scholarly article
title: Accurate and efficient computations of the Greeks for options near expiry using the Black-Scholes equations
zbMATH Open document ID: 1422.91703
DOI: 10.1155/2016/1586786
author: Darae Jeong
author: Minhyun Yoo
author: Junseok Kim
published in: Discrete Dynamics in Nature and Society
publication date: 2019-02-19T00:00:00Z
review text: Summary: 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.
Mathematics Subject Classification ID: 91G20
Mathematics Subject Classification ID: 91G60
zbMATH DE Number: 7025645
Wikidata QID: Q59123393
describes a project that uses: Matlab
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2016/1586786
OpenAlex ID: W2335910562
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description: scientific article; zbMATH DE number 7025645