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
N1 - Funding Information:
Thefirst author (Darae Jeong) was supported by a Korea University grant. The corresponding author (Junseok Kim) was supported by a subproject of the project Research for Applications of Mathematical Principles (no. C21501) and supported by the National Institute for Mathematical Sciences (NIMS)
Publisher Copyright:
© 2016 Darae Jeong et al.
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
U2 - 10.1155/2016/1586786
DO - 10.1155/2016/1586786
M3 - Article
AN - SCOPUS:84965160657
SN - 1026-0226
VL - 2016
JO - Discrete Dynamics in Nature and Society
JF - Discrete Dynamics in Nature and Society
M1 - 1586786
ER -