• Proceedings of the Korean Statistical Society Conference
• /
• 2004.11a
• /
• pp.165-170
• /
• 2004

This paper will derive explicit unified pricing formulas for eight types of outside barrier options, respectively. The monitoring periods of these options start at an arbitrary date and end at another arbitrary date before maturity. The eight types of barrier options are up-and-in, up-and-out, down-and-in and down-and-out call (or put) options.

• Communications of the Korean Mathematical Society
• /
• v.33 no.1
• /
• 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.

• Korean Journal of Mathematics
• /
• v.25 no.2
• /
• 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.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.5
• /
• pp.1497-1530
• /
• 2016

External barrier options are two-asset options with stochastic variables where the payoff depends on one underlying asset and the barrier depends on another state variable. The barrier state variable determines whether the option is knocked in or out when the value of the variable is above or below some prescribed barrier level. This paper derives the explicit analytic solution of the chained option with an external single or double barrier by utilizing the probabilistic methods - the reflection principle and the change of measure. Before we do this, we examine the closed-form solution of the external barrier option with a single or double-curved barrier using the methods of image and double Mellin transforms. The exact solution of the external barrier option price enables us to obtain the pricing formula of the chained option with the external barrier more easily.

• Communications of the Korean Mathematical Society
• /
• v.31 no.1
• /
• pp.199-207
• /
• 2016

A chained option is a barrier option activated in the event that the underlying asset price crosses barrier or barriers prior to maturity in a specified order. In this paper, we study the pricing of chained options with the quanto property called the "Quanto chained option". A quanto chained option is a chained option starting at time when the foreign exchange rate has the multiple crossing of specified barriers. We provide closed-form formulas for valuing the quanto chained options based on probabilistic approach.

• Communications of the Korean Mathematical Society
• /
• v.23 no.2
• /
• pp.285-294
• /
• 2008

A new Monte Carlo method is presented to compute the prices of barrier options on stocks. The key idea of the new method is to use an exit probability and uniformly distributed random numbers in order to efficiently estimate the first hitting time of barriers. It is numerically shown that the first hitting time error of the new Monte Carlo method decreases much faster than that of standard Monte Carlo methods.

• Journal of the Chungcheong Mathematical Society
• /
• v.33 no.1
• /
• 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.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2001.11a
• /
• pp.127-132
• /
• 2001

A successful design approach for noise barriers should be multidisciplinary because noise reduction goals influence both acoustical and non-acoustical considerations, such as maintenance, safety, physical construction, cost, and visual impact. These various barrier design options are closely related with barrier dimensions. In this study, we have proposed an optimal design method of straight noise barriers using genetic algorithm, providing a barrier having the smallest dimension and achieving the specified noise reduction at a receiver region exposed to the industry and traffic noise, to help a successful barrier design.

• Proceedings of the Korean Society for Noise and Vibration Engineering Conference
• /
• 2003.05a
• /
• pp.1020-1025
• /
• 2003

A successful design approach for noise barriers should be multidisciplinary because noise reduction goals influence both acoustical and non-acoustical considerations, such as maintenance, safety, physical construction, cost and visual impact These various barrier design options are closely related with barrier dimensions. In this study, we have proposed an optimal design method of noise barriers using simulated annealing algorithm, providing a barrier having the smallest dimension and achieving the specified noise reduction at a receiver region exposed to the industry and infrastructures, to help a successful barrier design.

• Industrial Engineering and Management Systems
• /
• v.10 no.2
• /
• pp.170-177
• /
• 2011

We present an improved binomial method for pricing financial deriva-tives by using cell averages. After non-overlapping cells are introduced around each node in the binomial tree, the proposed method calculates cell averages of payoffs at expiry and then performs the backward valuation process. The price of the derivative and its hedging parameters such as Greeks on the valuation date are then computed using the compact scheme and Richardson extrapolation. The simulation results for European and American barrier options show that the pro-posed method gives much more accurate price and Greeks than other recent lattice methods with less computational effort.