TY - JOUR
T1 - Super-Fast computation for the three-asset equity-linked securities using the finite difference method
AU - Lee, Chaeyoung
AU - Lyu, Jisang
AU - Park, Eunchae
AU - Lee, Wonjin
AU - Kim, Sangkwon
AU - Jeong, Darae
AU - Kim, Junseok
N1 - Funding Information:
Funding: The corresponding author (Junseok Kim) was supported by the Brain Korea 21 Plus (BK 21) from the Ministry of Education of Korea.
Publisher Copyright:
© 2020 by the authors.
PY - 2020/3/1
Y1 - 2020/3/1
N2 - In this article, we propose a super-fast computational algorithm for three-asset equity-linked securities (ELS) using the finite difference method (FDM). ELS is a very popular investment product in South Korea. There are one-, two-, and three-asset ELS. The three-asset ELS is the most popular financial product among them. FDM has been used for pricing the one-and two-asset ELS because it is accurate. However, the three-asset ELS is still priced using the Monte Carlo simulation (MCS) due to the curse of dimensionality for FDM. To overcome the limitation of dimension for FDM, we propose a systematic non-uniform grid with an explicit Euler scheme and an optimal implementation of the algorithm. The computational time is less than 6 s. We perform standard ELS option pricing and compare the results from the fast FDM with the ones from MCS. The computational results confirm the superiority and practicality of the proposed algorithm.
AB - In this article, we propose a super-fast computational algorithm for three-asset equity-linked securities (ELS) using the finite difference method (FDM). ELS is a very popular investment product in South Korea. There are one-, two-, and three-asset ELS. The three-asset ELS is the most popular financial product among them. FDM has been used for pricing the one-and two-asset ELS because it is accurate. However, the three-asset ELS is still priced using the Monte Carlo simulation (MCS) due to the curse of dimensionality for FDM. To overcome the limitation of dimension for FDM, we propose a systematic non-uniform grid with an explicit Euler scheme and an optimal implementation of the algorithm. The computational time is less than 6 s. We perform standard ELS option pricing and compare the results from the fast FDM with the ones from MCS. The computational results confirm the superiority and practicality of the proposed algorithm.
KW - Black-scholes equations
KW - Equity-linked securities
KW - Finite difference method
KW - Super-fast computation
UR - http://www.scopus.com/inward/record.url?scp=85082412826&partnerID=8YFLogxK
U2 - 10.3390/math8030307
DO - 10.3390/math8030307
M3 - Article
AN - SCOPUS:85082412826
SN - 2227-7390
VL - 8
JO - Mathematics
JF - Mathematics
IS - 3
M1 - 307
ER -