TY - JOUR
T1 - Computation of powered option prices under a general model for underlying asset dynamics
AU - Kim, Jerim
AU - Kim, Bara
AU - Kim, Jeongsim
AU - Lee, Sungji
N1 - Publisher Copyright:
© 2021 Elsevier B.V.
PY - 2022/5/1
Y1 - 2022/5/1
N2 - We derive the Laplace transforms for the prices and deltas of the powered call and put options, as well as for the price and delta of the capped powered call option under a general framework. These Laplace transforms are expressed in terms of the transform of the underlying asset price at maturity. For any model that can derive the transform of the underlying asset price, we can obtain the Laplace transforms for the prices and deltas of the powered options and the capped powered call option. The prices and deltas of the powered options and the capped powered call option can be computed by numerical inversion of the Laplace transforms. Models to which our method can be applied include the geometric Lévy model, the regime-switching model, the Black–Scholes–Vasiček model, and Heston's stochastic volatility model, which are commonly used for pricing of financial derivatives. In this paper, numerical examples are presented for all four models.
AB - We derive the Laplace transforms for the prices and deltas of the powered call and put options, as well as for the price and delta of the capped powered call option under a general framework. These Laplace transforms are expressed in terms of the transform of the underlying asset price at maturity. For any model that can derive the transform of the underlying asset price, we can obtain the Laplace transforms for the prices and deltas of the powered options and the capped powered call option. The prices and deltas of the powered options and the capped powered call option can be computed by numerical inversion of the Laplace transforms. Models to which our method can be applied include the geometric Lévy model, the regime-switching model, the Black–Scholes–Vasiček model, and Heston's stochastic volatility model, which are commonly used for pricing of financial derivatives. In this paper, numerical examples are presented for all four models.
KW - Black–Scholes–Vasiček model
KW - Geometric Lévy model
KW - Heston's stochastic volatility model
KW - Powered options
KW - Regime-switching model
UR - http://www.scopus.com/inward/record.url?scp=85122311386&partnerID=8YFLogxK
U2 - 10.1016/j.cam.2021.113999
DO - 10.1016/j.cam.2021.113999
M3 - Article
AN - SCOPUS:85122311386
SN - 0377-0427
VL - 406
JO - Journal of Computational and Applied Mathematics
JF - Journal of Computational and Applied Mathematics
M1 - 113999
ER -