Abstract
Two types of new methods with variable time steps are proposed in order to valuate binary options efficiently. Type I changes adaptively the size of the time step at each time based on the magnitude of the local error, while Type II combines two uniform meshes. The new methods are hybrid finite difference methods, namely starting the computation with a fully implicit finite difference method for a few time steps for accuracy then performing a θ-method during the rest of computation for efficiency. Numerical experiments for standard European vanilla, binary, and American options show that both Type I and II variable time step methods are much more efficient than the fully implicit method or hybrid methods with uniform time steps.
| Original language | English |
|---|---|
| Pages (from-to) | 413-426 |
| Number of pages | 14 |
| Journal | Bulletin of the Korean Mathematical Society |
| Volume | 48 |
| Issue number | 2 |
| DOIs | |
| Publication status | Published - 2011 Apr 29 |
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Keywords
- American options
- Binary options
- Hybrid finite difference method
- Option pricing
- Variable time steps
ASJC Scopus subject areas
- Mathematics(all)
Cite this
Variable time-stepping hybrid finite difference methods for pricing binary options. / Kim, Hongjoong; Moon, Kyoung Sook.
In: Bulletin of the Korean Mathematical Society, Vol. 48, No. 2, 29.04.2011, p. 413-426.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Variable time-stepping hybrid finite difference methods for pricing binary options
AU - Kim, Hongjoong
AU - Moon, Kyoung Sook
PY - 2011/4/29
Y1 - 2011/4/29
N2 - Two types of new methods with variable time steps are proposed in order to valuate binary options efficiently. Type I changes adaptively the size of the time step at each time based on the magnitude of the local error, while Type II combines two uniform meshes. The new methods are hybrid finite difference methods, namely starting the computation with a fully implicit finite difference method for a few time steps for accuracy then performing a θ-method during the rest of computation for efficiency. Numerical experiments for standard European vanilla, binary, and American options show that both Type I and II variable time step methods are much more efficient than the fully implicit method or hybrid methods with uniform time steps.
AB - Two types of new methods with variable time steps are proposed in order to valuate binary options efficiently. Type I changes adaptively the size of the time step at each time based on the magnitude of the local error, while Type II combines two uniform meshes. The new methods are hybrid finite difference methods, namely starting the computation with a fully implicit finite difference method for a few time steps for accuracy then performing a θ-method during the rest of computation for efficiency. Numerical experiments for standard European vanilla, binary, and American options show that both Type I and II variable time step methods are much more efficient than the fully implicit method or hybrid methods with uniform time steps.
KW - American options
KW - Binary options
KW - Hybrid finite difference method
KW - Option pricing
KW - Variable time steps
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U2 - 10.4134/BKMS.2011.48.2.413
DO - 10.4134/BKMS.2011.48.2.413
M3 - Article
AN - SCOPUS:79955138008
VL - 48
SP - 413
EP - 426
JO - Bulletin of the Korean Mathematical Society
JF - Bulletin of the Korean Mathematical Society
SN - 1015-8634
IS - 2
ER -