• Journal of the Korean Mathematical Society
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• v.43 no.2
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• pp.357-371
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• 2006

Let $X\;=\;(X_t,\;t{\in}[0, T])$ be a generalized Brownian motion(gBm) determined by mean function a(t) and variance function b(t). Let $L^2({\mu})$ denote the Hilbert space of square integrable functionals of $X\;=\;(X_t - a(t),\; t {in} [0, T])$. In this paper we consider a class of nonlinear functionals of X of the form F(. + a) with $F{in}L^2({\mu})$ and discuss their analysis. Firstly, it is shown that such functionals do not enjoy, in general, the square integrability and Malliavin differentiability. Secondly, we establish regularity conditions on F for which F(.+ a) is in $L^2({\mu})$ and has its Malliavin derivative. Finally we apply these results to compute the price and the hedging portfolio of a contingent claim in our financial market model based on a gBm X.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.18 no.1
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• pp.61-74
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• 2014

This paper presents accurate and efficient numerical methods for calculating the sensitivities of two-asset European options, the Greeks. The Greeks are important financial instruments in management of economic value at risk due to changing market conditions. The option pricing model is based on the Black-Scholes partial differential equation. The model is discretized by using a finite difference method and resulting discrete equations are solved by means of an operator splitting method. For Delta, Gamma, and Theta, we investigate the effect of high-order discretizations. For Rho and Vega, we develop an accurate and robust automatic algorithm for finding an optimal value. A cash-or-nothing option is taken to demonstrate the performance of the proposed algorithm for calculating the Greeks. The results show that the new treatment gives automatic and robust calculations for the Greeks.

• The Korean Journal of Financial Management
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• v.23 no.2
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• pp.209-237
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• 2006

Since previous default forecasting models for the firms evaluate the probability of default based upon the accounting data from book values, they cannot reflect the changes in markets sensitively and they seem to lack theoretical background. The market-information based models, however, not only make use of market data for the default prediction, but also have strong theoretical background like Black-Scholes (1973) option theory. So, many firms recently use such market based model as KMV to forecast their default probabilities and to manage their credit risks. Korean firms also widely use the KMV model in which default point is defined by liquid debt plus 50% of fixed debt. Since the debt structures between Korean and American firms are significantly different, Korean firms should carefully use KMV model. In this study, we empirically investigate the importance of debt structure. In particular, we find the following facts: First, in Korea, fixed debts are more important than liquid debts in accurate prediction of default. Second, the percentage of fixed debt must be less than 20% when default point is calculated for Korean firms, which is different from the KMV. These facts give Korean firms some valuable implication about default forecasting and management of credit risk.

• Journal of the Korea Institute of Information and Communication Engineering
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• v.26 no.10
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• pp.1423-1431
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• 2022

Volatility is one of the variables that the Black-Scholes model requires for option pricing. It is an unknown variable at the present time, however, since the option price can be observed in the market, implied volatility can be derived from the price of an option at any given point in time and can represent the market's expectation of future volatility. Although volatility in the Black-Scholes model is constant, when calculating implied volatility, it is common to observe a volatility smile which shows that the implied volatility is different depending on the strike prices. We implement supervised learning to target implied volatility by adding V-KOSPI to ease volatility smile. We examine the estimation performance of KOSPI200 index options' implied volatility using various Machine Learning algorithms such as Linear Regression, Tree, Support Vector Machine, KNN and Deep Neural Network. The training accuracy was the highest(99.9%) in Decision Tree model and test accuracy was the highest(96.9%) in Random Forest model.

• The Korean Journal of Financial Management
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• v.14 no.2
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• pp.21-55
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• 1997

본 연구는 기업규모, 장부가치/시장가치 비율, 순이익/주가 비율, 현금흐름/주가 비율, 레버리지 등 기본적 변수를 사용하여 주식수익률에 유의적인 변수를 확인하고, 또한 Fama and French(1993) 등에 의해서 제시된 다요인모형(multi-factor model)이 한국주식시장에서 적용가능한 지를 살펴보았다. 이를 위하여 본 연구에서는 Fama and MacBeth(1973)의 횡단면회귀모형과 Black, Jensen, and Scholes (1972)의 시계열모형을 사용하였으며, 실증분석결과를 요약하면 다음과 같다. 먼저 횡단면분석결과에 의하면, 장부가치/시장가치 비율(BE/ME), 현금흐름/주가 비율(C/P) 등이 주식수익률의 횡단면적 차이를 설명할 수 있는 유의적인 변수로 나타났다. 그리고 통계적 의미에서는 1월효과가 존재한다고 보기 어려우나, 경제적 의미에서 1월효과가 존재하는 것으로 생각된다. 시계열분석결과에 의하면, 시장요인, 기업규모요인, 장부가치/시장가치요인(또는 현금흐름/주가요인) 등의 3요인에 의해서 국내 주식수익률의 공통적 변동을 잘 설명할 수 있다. 즉 국내 증권시장에서도 Fama and French(1993)의 3요인모형이 성립될 수 있는 것으로 판단된다.

• The Korean Journal of Applied Statistics
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• v.25 no.5
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• pp.757-773
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• 2012

Traditional value at risk(S-VaR) has a difficulity in predicting the future risk of financial asset prices since S-VaR is a backward looking measure based on the historical data of the underlying asset prices. In order to resolve the deficiency of S-VaR, an economic value at risk(E-VaR) using the risk neutral probability distributions is suggested since E-VaR is a forward looking measure based on the option price data. In this study E-VaR is estimated by assuming the generalized gamma distribution(GGD) as risk neutral density function which is implied in the option. The estimated E-VaR with GGD was compared with E-VaR estimates under the Black-Scholes model, two-lognormal mixture distribution, generalized extreme value distribution and S-VaR estimates under the normal distribution and GARCH(1, 1) model, respectively. The option market data of the KOSPI 200 index are used in order to compare the performances of the above VaR estimates. The results of the empirical analysis show that GGD seems to have a tendency to estimate VaR conservatively; however, GGD is superior to other models in the overall sense.

• Industrial Engineering and Management Systems
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• v.9 no.4
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• pp.323-338
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• 2010

In this paper, we introduce the implied volatility from Black-Scholes model and suggest a model for constructing implied volatility surfaces by using the two-dimensional cubic (bi-cubic) spline. In order to utilize a spline method, we acquire grid (knot) points. To this end, we first extract implied volatility curves weighted by trading contracts from market option data and calculate grid points from the extracted curves. At this time, we consider several conditions to avoid arbitrage opportunity. Then, we establish an implied volatility surface, making use of the two-dimensional cubic spline method with previously estimated grid points. The method is shown to satisfy several properties of the implied volatility surface (smile, skew, and flattening) as well as avoid the arbitrage opportunity caused by simple match with market data. To show the merits of our proposed method, we conduct simulations on market data of S&P500 index European options with reasonable and acceptable results.

• Journal of Advanced Navigation Technology
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• v.15 no.1
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• pp.104-111
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• 2011

In this study, I have tried to analyze an influence of R&D investment on ROV(Real Option Value), corporate value and market value by analyzing R&D investment, ROV, corporate value and market value of machine and material industry in the perspective of ex post. As a result of this study, corporate value, which has been deduced by real option according to R&D investment, reflects market value well and possesses a strong correlation with R&D investment, ROV, corporate value and market value. This implication demonstrates this study result is corresponding with existing theories.

• 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.

• The Korean Journal of Applied Statistics
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• v.24 no.6
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• pp.1007-1020
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• 2011

Since the research of Black and Scholes (1973), modeling methods using diffusion processes have performed principal roles in financial engineering. In modern financial theories, various types of diffusion processes were suggested and applied in real situations. An estimation of the model parameters is an indispensible step to analyze financial data using diffusion process models. Many estimation methods were suggested and their properties were investigated. This paper reviews the statistical properties of the, Euler approximation method, New Local Linearization(NLL) method, and Generalized Methods of Moment(GMM) that are known as the most practical methods. From the simulation study, we found the NLL and Euler methods performed better than GMM. GMM is frequently used to estimate the parameters because of its simplicity; however this paper shows the performance of GMM is poorer than the Euler approximation method or the NLL method that are even simpler than GMM. This paper shows the performance of the GMM is extremely poor especially when the parameters in diffusion coefficient are to be estimated.