• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.12 no.4
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• pp.271-287
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• 2008

This paper deals with American call and put options. Determining the fair price and the free boundary of an American option is a very difficult problem since they depends on each other. This paper presents numerical algorithms of finite element method based on the three-level scheme to compute both the price and the free boundary. One algorithm is designed for American call options and the other one for American put options. These algorithms are formulated on the system of the Jamshidian equation for the option price and the free boundary. Here, the Jamshidian equation is of a kind of the nonhomogeneous Black-Scholes equations. We prove the existence and uniqueness of the numerical solution by the Lax-Milgram lemma and carried out extensive numerical experiments to compare with various methods.

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

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.4 no.2
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• pp.11-20
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• 2000

This paper presents a formula that relates the optimal exercise boundaries of American call and put options on futures contract. It is shown that the geometric mean of the optimal exercise boundaries for call and put written on the same futures contract with the same exercise price is equal to the exercise price which is time invariant. The paper also investigates the properties of American calls and puts on futures contract.

• The Korean Journal of Financial Studies
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• v.3 no.1
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• pp.213-231
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• 1996

In this study we conduct a specification test of at-the-money option volatility. Results show that the implied volatility estimate recovered from the Black-Scholes European option pricing model is nearly indistinguishable from the implied volatility estimate obtained from the Barone-Adesi and Whaley's American option pricing model. This study also investigates whether the use of Black-Scholes implied volatility estimates in American put pricing model significantly affect the prediction the prediction of American put option prices. Results show that, at long as the possibility of early exercise is carefully controlled in calculation of implied volatilities prediction of American put prices is not significantly distorted. This suggests that at-the-money option implied volatility estimates are robust across option pricing model.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.2
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• pp.151-160
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• 2011

Typically, it is hard to find a closed form solution of option pricing formula under an asset governed by a change point process. In this paper we derive a closed-form solution of the valuation function for an American perpetual put option under an asset having a change point. Structural changes are formulated through a change-point process with a Markov chain. The modified smooth-fit technique is used to obtain the closed-form valuation function. We also guarantee the optimality of the solution via the proof of a corresponding verification theorem. Numerical examples are included to illustrate the results.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.1
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• pp.1-21
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• 2015

This paper presents two algorithms based on the Jamshidian equation which is from the Black-Scholes partial differential equation. The first algorithm is for American call options and the second one is for American put options. They compute numerically free boundary and then option price, iteratively, because the free boundary and the option price are coupled implicitly. By the upwind finite-difference scheme, we discretize the Jamshidian equation with respect to asset variable s and set up a linear system whose solution is an approximation to the option value. Using the property that the coefficient matrix of this linear system is an M-matrix, we prove several theorems in order to formulate a bisection method, which generates a sequence of intervals converging to the fixed interval containing the free boundary value with error bound h. These algorithms have the accuracy of O(k + h), where k and h are step sizes of variables t and s, respectively. We prove that they are unconditionally stable. We applied our algorithms for a series of numerical experiments and compared them with other algorithms. Our algorithms are efficient and applicable to options with such constraints as r > d, $r{\leq}d$, long-time or short-time maturity T.

• English & American cultural studies
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• v.10 no.2
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• pp.29-48
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• 2010

This paper is a kind of interdisciplinary studies which connect a Western film criticism with a criticism of minority literature in America. My purpose in this paper is to put on the table such a sensitive issue as racial representation and representativeness in Clint Eastwood's revisionist Western, Unforgiven. We admit generally that Western films have contributed to the white American myth-making of how the West was won. Yet, since the mid-1960s, a growing number of revisionist Westerns were produced so as to raise a question about the conventional way of looking at what happened in the American West. In order to analyze the problem inherent in the way of seeing, I pay attention to how the director Eastwood (re)presents a character named W. W. Beauchamp in the film. Presumably, what the character Beauchamp misses in the West can be overlapped with what ordinary film viewers miss in the genre of Westerns. Given this, interrogating both what Beauchamp sees and what he misses within the movie, I attempt to disclose how much of the West has been unseen from his biased viewpoint. By doing so, I argue why it is important to focus on some passing scenes that touch on the irony of a Native American train passenger, the gaze of the mute Native American housewife, the abrupt disappearance of Asian American men, the lynching of African-American ex-cowboy, and the self-determination of the saloon prostitutes. Then I hope that, conservative and mainstream though the director is, his way of revising the Western is not quite far from my minority-conscious critical position.

• Bulletin of the Korean Mathematical Society
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• v.48 no.4
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• pp.791-812
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• 2011

This is a survey on American options. An American option allows its owner the privilege of early exercise, whereas a European option can be exercised only at expiration. Because of this early exercise privilege American option pricing involves an optimal stopping problem; the price of an American option is given as a free boundary value problem associated with a Black-Scholes type partial differential equation. Up until now there is no simple closed-form solution to the problem, but there have been a variety of approaches which contribute to the understanding of the properties of the price and the early exercise boundary. These approaches typically provide numerical or approximate analytic methods to find the price and the boundary. Topics included in this survey are early approaches(trees, finite difference schemes, and quasi-analytic methods), an analytic method of lines and randomization, a homotopy method, analytic approximation of early exercise boundaries, Monte Carlo methods, and relatively recent topics such as model uncertainty, backward stochastic differential equations, and real options. We also provide open problems whose answers are expected to contribute to American option pricing.

• Journal of Families and Better Life
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• v.27 no.5
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• pp.183-194
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• 2009

The purpose of this study was to explore the ideas about Korean-American mother's school-age child rearing that are represented on internet community. The method used for this study was content analysis and the data consisted of articles about Korean-American mother's school-age child rearing on a internet community bulletin board during 1 year in 2008. It was found that these articles dealt with problems of practice in interfacing between home and social institutions(Especially school), teaching, counseling, nurturing and disciplining. For example, 831 articles put great emphasis on interfacing between home and social institutions, 339 on teaching, 268 on counseling with children. From these results, we might conclude that many Korean-American mothers gave their children school related care.

• Journal of the Korean Home Economics Association
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• v.24 no.3
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• pp.31-42
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• 1986

It is generallybelieved that the values of female students are different depending on the cultural enviromment of society. The purpose of this paper is to discern the value orientation of female students in Korea and America, and how they are related to the clothing behavior. 300 female students were selected as sample from the Univ. of Minnesota and 158 students filled out the questionnair. 420 female students were selected from five unversities in Jinju, Taegy and Pusan. RESULTS : 1) Korean students had highly evaluated theaethetic, political, religious and social values, and American students had higher evaluation on the economic and American students had higher evaluation on the economic and theoretical values. 2) Korean students tended to regard modesty, conformity and management as important factors when they chose new clothes, and for American students, appearance and tool were important. 3) The impact of values on clothing vehavior was as follows. a) Korean students who emphasized theoretical values did not use clothes as an instrument of status symbol and modesty. b) American students who emphasized the economic values tended to have an interest in purchase and wearing of clothes on purpose. c) Korean students who had positive attitudes on the aethetic values tended to be conservative, but they wanted to use the clothes as a demonstration of self exaggeraton. d) Korean students who regarded social values important tended to have a higher interest in the management of clothes. e) Korean students who had highly evaluated the religious values tended to be conservative when the selected new clothes. American students did not want to conform to the group norm when they chose new clothes. On the whole, American students did not put on clothes to achieve a specific goal. In short, it can be concluded that Korean students and American students have different values and they have a great impact on their clothing behavior.