• Korean Journal of Mathematics
• /
• 제25권2호
• /
• pp.229-246
• /
• 2017

This paper concerns barrier option of American type where the underlying price is monitored during only part of the option's life. Analytic valuation formulas of the American partial barrier options are obtained by approximation method. This approximation method is based on barrier options along with exponential early exercise policies. This result is an extension of Jun and Ku [10] where the exercise policies are constant.

• 대한수학회논문집
• /
• 제33권1호
• /
• pp.345-360
• /
• 2018

In finance, barrier options are options contracts with a payoff that depends on whether the price of the underlying asset hits a predetermined barrier level during the option's lifetime. Based on exotic options and random fluctuations of interest rates in the marketplace, we consider discount barrier options with a stochastic interest rate driven by the Hull-White process. This paper derives the closed-form solutions of the discount barrier option and the discount double barrier option using Mellin transform methods and the PDE (partial differential equation) method of images.

• Journal of applied mathematics & informatics
• /
• 제29권5_6호
• /
• pp.1501-1509
• /
• 2011

In this study, assume that the stock price obeys the stochastic differential equation driven by mixed fractional Brownian motion, and the short rate follows the Vasicek model. Then, the Black-Scholes partial differential equation is held by using fractional Ito formula. Finally, the pricing formulae of the barrier option are obtained by partial differential equation theory. The results of Black-Scholes model are generalized.

• 한국통계학회:학술대회논문집
• /
• 한국통계학회 2003년도 추계 학술발표회 논문집
• /
• pp.73-78
• /
• 2003

This presentation derives a distribution function of the terminal value and running maximum of two-dimensional Brownian motion {X(t) = (X$_1$(t), X$_2$(T))', t > 0}. One random variable of the joint distribution is the terminal time value of the Brownian motion {X$_1$(t), t > 0}. The other random variable is the partial-time running maximum of the Brownian motion {X$_2$(t), t > 0}. With this distribution function, this presentation also derives an explicit pricing formula for a barrier option whose monitoring period of the option starts at an arbitrary date and ends at another arbitrary date before maturity.

• 충청수학회지
• /
• 제33권1호
• /
• pp.165-171
• /
• 2020

In this paper we consider a mixed fractional Brownian motion (mfBm) with jumps. The prices of European barrier options can be evaluated by solving a partial integro-differential equation (PIDE) with variable coefficients, which is derived from the mfBm with jumps. The 2-step backward differentiation formula (BDF2 method) proposed in [6] is applied with the second-order convergence rate in the time and spatial variables. Numerical simulations are carried out to observe the convergence behaviors of the BDF2 method under the mfBm with the Kou model.

• 한국진공학회:학술대회논문집
• /
• 한국진공학회 2013년도 제45회 하계 정기학술대회 초록집
• /
• pp.214.2-214.2
• /
• 2013

Device performance for the 45 and 32 nm node CMOS technology requires the integration of ultralow-k materials. To lower the dielectric constant for PECVD and spin-on materials, partial replacement of the solid network with air (k=1.01) appears to be more intuitive and direct option. This can be achieved introducting of second "labile" phase during depositoin that is removed during a subsequent UV curing and annealing step. Besides, with shrinking line dimensions the resistivity of barrier films cannot meet the International Technology Roadmap for Semiconductors (ITRS) requirements. To solve this issue self-forming diffusion barriers have drawn attention for great potential technique in meeting all ITRS requirments. In this present work, we report a Cu-V alloy as a materials for the self-forming barrier process. And we investigated diffusion barrier properties of self-formed layer on low-k dielectrics with or without UV curing treatment. Cu alloy films were directly deposited onto low-k dielectrics by co-sputtering, followed by annealing at various temperatures. X-ray diffraction revealed Cu (111), Cu (200) and Cu (220) peaks for both of Cu alloys. The self-formed layers were investigated by transmission electron microscopy. In order to compare barrier properties between V-based interlayer on low-k dielectric with UV curing and interlayer on low-k dielectric without UV curing, thermal stability was measured with various heat treatment temperature. X-ray photoelectron spectroscopy analysis showed that chemical compositions of self-formed layer. The compositions of the V based self-formed barriers after annealing were strongly dominated by the O concentration in the dielectric layers.