• Communications of the Korean Mathematical Society
• /
• v.13 no.2
• /
• pp.367-375
• /
• 1998

In this paper, we present the close solution for minimal hedging portofolis $II^*$ when payment f for American option admits the integral option.

• Journal of the Chungcheong Mathematical Society
• /
• v.29 no.3
• /
• pp.503-508
• /
• 2016

We propose a number of finite difference methods for the prices of a European option under the CGMY model. These numerical methods to solve a partial integro-differential equation (PIDE) are based on three time levels in order to avoid fixed point iterations arising from an integral operator. Numerical simulations are carried out to compare these methods with each other for pricing the European option under the CGMY model.

• Bulletin of the Korean Mathematical Society
• /
• v.58 no.2
• /
• pp.349-364
• /
• 2021

This paper studies the optimal surrender policies for a variable annuity (VA) contract with a surrender option and a fixed insurance fee for guaranteed minimum maturity benefits (GMMB). In our proposed model, a policyholder pays the fixed insurance fee. Based on the integral transform techniques, we derive the analytic integral equations for the optimal surrender boundary and the value function of the VA contract that can be solved numerically by recursive integration method. We provide numerical values for the value function, the optimal surrender boundary, and the expected optimal surrender time.

• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.15 no.1
• /
• pp.31-41
• /
• 2011

I introduce a derivative called "Snowball Currency Option" or "USDKRWSnowball Extendible At Expiry KO" which was traded once in the over-the-counter market in Korea. A snowball currency option consists of a series of maturities the payoffs at which are like those of a long position in a put option and two short position in an otherwise identical call. The strike price at each maturity depends on the exchange rate and the previous strike price so that the strike prices are random and path-dependent, which makes it difficult to find a closed form solution of the value of a snowball currency option. I analyze the payoff structure of a snowball currency option and derive an upper and a lower boundaries of the value of it in a simplified model. Furthermore, I derive a pricing formula using integral in the simplified model.

• Bulletin of the Korean Mathematical Society
• /
• v.53 no.5
• /
• pp.1411-1425
• /
• 2016

We provide a partial differential equation for European options on a stock whose price process follows a general geometric Riemannian Brownian motion. The existence and the uniqueness of solutions to the partial differential equation are investigated, and then an expression of the value for European options is obtained using the fundamental solution technique. Proper Riemannian metrics on the real number field can make the distribution of return rates of the stock induced by our model have the character of leptokurtosis and fat-tail; in addition, they can also explain option pricing bias and implied volatility smile (skew).

• Journal of The Korean Association For Science Education
• /
• v.35 no.1
• /
• pp.121-130
• /
• 2015

Identifying students' achievement level and reflecting it on educational policy making or instructional improvement by analyzing the results of nationwide standardized assessment is an integral part of accountability in education. On the basis of this premise, we analyzed the characteristics of National Assessment of Educational Achievement (NAEA) items for middle school science subject conducted from 2010 to 2013 by using the option response rate distribution curve, the fittest graph estimated from the response rate of correct/incorrect options by achievement score. Furthermore, we classified the type of option response rate curve in terms of correct and incorrect options. Results of the analysis of option response curve showed that five types of correct option response curve (S-shaped, J-shaped, straight-shaped, F-shaped, and step-shaped) and 4 types of incorrect option response curve (down-slope, flat, mound, and up-slope) were identified. The most common type of items was the combination of S-shaped correct option response curve and down-slope incorrect option response curve, which are considered as appropriate items to discriminate the students according to achievement level. Moreover, correct option response was found to be correlated with incorrect option response. Based on the results, we also discussed some implications on teaching-learning method and classroom assessment in science education.

• Journal of Korean Institute of Industrial Engineers
• /
• v.38 no.4
• /
• pp.244-248
• /
• 2012

We present a simple numerical method for pricing American put options under a constant elasticity of variance (CEV) model. Our analysis is done in a general framework where only the risk-neutral transition density of the underlying asset price is given. We obtain an integral equation of early exercise premium. By exploiting a modification of the integral equation, we propose a novel and simple numerical iterative valuation method for American put options.

• Proceedings of the Korean Statistical Society Conference
• /
• 2003.05a
• /
• pp.79-84
• /
• 2003

Likelihood estimation in random-effect models is often complicated because the marginal likelihood involves an analytically intractable integral. Numerical integration such as Gauss-Hermite quadrature is an option, but is generally not recommended when the dimensionality of the integral is high. An alternative is the use of hierarchical likelihood, which avoids such burdensome numerical integration. These two approaches for fitting binary data are compared and the advantages of using the hierarchical likelihood are discussed. Random-effect models for binary outcomes and for bivariate binary-continuous outcomes are considered.

• The Pure and Applied Mathematics
• /
• v.22 no.2
• /
• pp.159-168
• /
• 2015

Abstract. We propose a fast and robust finite difference method for Merton's jump diffusion model, which is a partial integro-differential equation. To speed up a computational time, we compute a matrix so that we can calculate the non-local integral term fast by a simple matrix-vector operation. Also, we use non-uniform grids to increase efficiency. We present numerical experiments such as evaluation of the option prices and Greeks to demonstrate a performance of the proposed numerical method. The computational results are in good agreements with the exact solutions of the jump-diffusion model.

• The Pure and Applied Mathematics
• /
• v.27 no.4
• /
• pp.231-249
• /
• 2020

We present an efficient and robust finite difference method for a two-asset jump diffusion model, which is a partial integro-differential equation (PIDE). To speed up a computational time, we compute a matrix so that we can calculate the non-local integral term fast by a simple matrix-vector operation. In addition, we use bilinear interpolation to solve integral term of PIDE. We can obtain more stable value by using the payoff-consistent extrapolation. We provide numerical experiments to demonstrate a performance of the proposed numerical method. The numerical results show the robustness and accuracy of the proposed method.