• The Korean Journal of Financial Management
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• v.21 no.2
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• pp.211-233
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• 2004

This purpose of paper is to propose a European option pricing formula when the rate of return follows the leptokurtic distribution instead of normal. This distribution explains well the volatility smile and furthermore the option prices calculated under the leptokurtic distribution are shown to be closer to the market prices than those of Black-Scholes model. We make an estimation of the implied volatility and kurtosis to verify the fitness of the pricing formula that we propose here.

• International Journal of Naval Architecture and Ocean Engineering
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• v.13 no.1
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• pp.367-378
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• 2021

This paper develops a dynamic regression model to quantify the contribution of key external factors to operational energy efficiency of ships. On this basis, kernel density estimation is applied to explore distribution patterns of fluctuations in operational performance. An empirical analysis based on these methods show that distribution of fluctuations in Energy Efficiency Operational Indicator (EEOI) is leptokurtic and fat tailed, rather than a normal one. Around 85% of fluctuations in EEOI can be jointly explained by capacity utilization and sailing speed, while the rest depend on other external factors largely beyond control. The variations in capacity utilization and sailing speed cannot be fully passed on to the energy efficiency performance of ships, due to complex interactions between various external factors. The application of the methods is demonstrated, showing a potential approach to develop a rating mechanism for use in the legally binding framework on operational energy efficiency of ships.

• The Korean Journal of Financial Management
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• v.20 no.1
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• pp.213-231
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• 2003

This paper uses the Efficient Method of Moments(EMM) of Gallant and Tauchen to estimate continuous-time stochastic volatility diffusion model for the Korean Composite Stock Price Index, sampled daily over $1995\sim2002$. The estimates display non-normality of stock index return, leptokurtic distribution, and stochastic volatility. Funker, this study suggests that two factor stochastic volatility model will be more desirable than one factor stochastic volatility model to estimate daily Korean stock return and also suggests that the stochastic volatility diffusions should allow for Poisson jumps of time-varying intensity.

• The Korean Journal of Applied Statistics
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• v.27 no.6
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• pp.1039-1047
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• 2014

An autoregressive model with normal errors is a natural model that attempts to fit time series data. More flexible models that include normal distribution as a special case are necessary because they can cover normality to non-normality models. The skewed exponential power distribution is a possible candidate for autoregressive models errors that may have tails lighter(platykurtic) or heavier(leptokurtic) than normal and skewness; in addition, the use of skewed exponential power distribution can reduce the influence of outliers and consequently increases the robustness of the analysis. We use SIR algorithm and grid method for an efficient Bayesian estimation.

• The Korean Journal of Financial Management
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• v.21 no.1
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• pp.149-181
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• 2004

In this study we perform empirical tests using KOSPI return to investigate the existence of nonlinear characteristics in the generating process of stock returns. There are three categories in empirical tests; the test of nonlinear dependence, nonlinear stochastic process and nonlinear deterministic chaos. According to the analysis of nonlinearity, stock returns are not normally distributed but leptokurtic, and appear to have nonlinear dependence. And it's decided that the nonlinear structure of stock returns can not be completely explained using nonlinear stochastic models of ARCH-type. Nonlinear deterministic chaos system is the feedback system, which the past incidents influence the present, and it is the fractal structure with self-similarity and has the sensitive dependence on initial conditions. To summarize the results of chaos analysis for KOSPI return, it is the persistent time series, which is not IID and has long memory, takes biased random walk, and is estimated to be fractal distribution. Also correlation dimension, as the approximation of fractal dimension, converged stably within 3 and 4, and maximum Lyapunov exponent has positive value. This suggests that chaotic attractor and the sensitive dependence on initial conditions exist in stock returns. These results fit into the characteristics of chaos system. Therefore it's decided that the generating process of stock returns has nonlinear deterministic structure and follow chaotic process.

• Journal of Plant Biology
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• v.24 no.1
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• pp.47-57
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• 1981

Girth at breast height was measured to test skewness ($g_1$) and kurtosis ($g_2$) of frequency distribution of the basal area in terms of t-test and Kolmogorov-Smirnov test for a total of forty six monocultures within Sudong and Kwhangnung area in central part of Korean peninsula in 1979 and 1980. The monocultures are about 10 to 50 years old, and four kinds: Pinus koraiensis, Larix kaempferi, Abies holophylla and Pinus rigida. Most of the sample sizes per site were ranged 70 to 110 excluding 4 sites. The number of classes interval was based on Sturges rule for each monoculture and was ranged from 5 to 10. In Sudong the range of age(yr) and basal area (($cm^2$)/tree) of the monocultures were from 10 to 20 and from 27.60 to 383. for Kwhangnung they were from 15 to 47 and mostly 102.15 to 619.14, respectively. All 43 monocultures except 1 showed +$g_1$, which ranged from 0.3 to 2.2 except six sites. Of the total 46 sites, 23 sites showed significant +$g_1$ which includes about 10 year-old monoculture. The number of classes interval with significant positive skewness ranged from 6 to 9. The data suggest that intraspecific competition in terms of stand structure seems to appear from about 10 year-old monocultures, and it may even last to about 50 year-old one. Around 24 monocultures showed nonsignificant -$g_2$ except one. Most -$g_2$ ranged from -0.12 to -0.83. Around 20 monocltures showed positive $g_2$ ranging from +0.13 to +3.841. Of the 22 +$g_1$, majority of 11 were very highly significant. Of all monocultures only 5 showed significant result from Kolmogorov-Smirnov test. Of the 4 species, Larix kaempferi seems to show density stress first then Abies holophylla, and Pinus koraiensis last. Data of this study indicate that adequate number of classes intervals and sample sizes for studying intraspecific competition in terms of basal area are 6 to 9 and 80 trees rather than 12 and 100 trees, respectively. It also suggests that most of the frequency distribution of basal area class are trimodal rather than bimodal under density stress. It is proposed that the leptokurtic distribution appears before normal distribution rather than direct change from platykurtic to normal distribution of basal area for selected stages in the development of stands.

• Wind and Structures
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• v.35 no.1
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• pp.21-34
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• 2022

Gust factor is an important parameter for the conversion between peak gust wind and mean wind speed used for the structural design and wind-related hazard mitigation. The gust factor of typhoon wind is observed to show a significant dispersion and some differences with large-scale weather systems, e.g., monsoons and extratropical cyclones. In this study, insitu measurement data captured by 13 meteorological towers during a strong typhoon Morakot are collected to investigate the statistical characteristics, height and wind speed dependency of the gust factor. Onshore off-sea and off-land winds are comparatively studied, respectively to characterize the underlying terrain effects on the gust factor. The theoretical method of peak factor based on Gaussian assumption is then introduced to compare the gust factor profiles observed in this study and given in some building codes and standards. The results show that the probability distributions of gust factor for both off-sea winds and off-land winds can be well described using the generalized extreme value (GEV) distribution model. Compared with the off-land winds, the off-sea gust factors are relatively smaller, and the probability distribution is more leptokurtic with longer tails. With the increase of height, especially for off-sea winds, the probability distributions of gust factor are more peaked and right-tailed. The scatters of gust factor decrease with the mean wind speed and height. AS/NZ's suggestions are nearly parallel with the measured gust factor profiles below 80m, while the fitting curve of off-sea data below 120m is more similar to AIJ, ASCE and EU.

• Phonetics and Speech Sciences
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• v.15 no.3
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• pp.17-25
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• 2023

This study examines the fundamental frequency(f0) distribution of 2,740 Korean speakers in a dialogue speech corpus. Praat and R were used for the collection and analysis of acoustical f0 data after removing extreme values considering the interquartile f0 range of the intonational phrases produced by each individual speaker. Results showed that the average f0 value of all speakers was 185 Hz and the median value was 187 Hz. The f0 data showed a positively skewed distribution of 0.11, and the kurtosis was -0.09, which is close to the normal distribution. The pitch values of daily conversations varied in the range of 238 Hz. Further examination of the male and female groups showed distinct median f0 values: 114 Hz for males and 199 Hz for females. A t-test between the two groups yielded a significant difference. The skewness representing the distribution shape was 1.24 for the male group and 0.58 for the female group. The kurtosis was 5.21 and 3.88 for the male and female groups, and the male group values appeared leptokurtic. A regression analysis between the median f0 and age yielded a slope of 0.15 for the male group and -0.586 for the female group, which indicated a divergent relationship. In conclusion, a normative f0 distribution of different Korean age and sex groups can be examined in the conversational speech corpus recorded by a massive number of participants. However, more rigorous data might be required to define a relation between age and f0 values.

• Journal of the Korean Data and Information Science Society
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• v.28 no.2
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• pp.251-260
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• 2017

The option pricing of Black와 Scholes (1973) and Merton (1973) has been widely reported to fail to reflect the time varying volatility of financial time series in many real applications. For example, Duan (1995) proposed GARCH option pricing method through Monte Carlo simulation. However, financial time series is known to follow a fat-tailed and leptokurtic probability distribution, which is not explained by Duan (1995). In this paper, in order to overcome such defects, we proposed the option pricing method based on GARCH models with normal mixture errors. According to the analysis of KOSPI200 option price data, the option pricing based on GARCH models with normal mixture errors outperformed the option pricing based on GARCH models with normal errors in the unstable period with high volatility.

• 한국해양학회지
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• v.22 no.3
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• pp.130-142
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• 1987

Sedimentological characteristics of the surface sediments in the southern sea off Cheju Island are described from analyses of bottom sediments. The sediments are subdivided into seven textural classes, muddy sand, slightly gravelly muddy sand, sand, clayey sand, sandy clay, sandymud, silty sand. Sand-size sediments are distributed in the southeastern part and/or around the Island, whereas sandy and muddy sediments are mainly distributed in the central and southern parts of the study area. A small portion of mud patch is located in the southwestern part of the area. According to the textural parameters analysis, sediments in the study area are poorly sorted(av.2.52 ), positive skewed(av.1.61 ), leptokurtic(av.1.74 ), transported by saltation and/or suspension, and roundness of quartz is varied from angular to surrounded, which suggesting that the depositional environment is not simple. The calcium carbonate content is on the average 26.99%, and commonly abundant in sand-size sediments, whereas organic matter content in the bulk sediment is on the average 6.70% and usually dominant in fine-grained sediments.Light minerals consist of quartz(av56.01%),Na-Ca feldspar(av.6.15%),K-feldspar(av.9.22%) and rock fragments(av28.11%).The contect onquartz and K-feldspar increases continuously away from the Cheju Island. As a result of geochemical analysis,concentrations of the elements are as follow:Zn:19.42-43.52 ppm (av.30.67ppm),Mn:50-304 ppm(av139.39ppm),Cr:3.54-10.68ppm(av6.50ppm),Pb:5.52-41.68ppm(av.15.60ppm), Co:7.08-14.68ppm (av.10.78ppm),Ni:19.70-42.42ppm(av.29.57ppm),Cu:3.14-9.12ppm(av.5.14ppm),Fe:0.48-2.08% (av1.22%),Ca:0.32-13.16%(av6.60%),Al:0.06-0.08%(av.0.27%),Mg:0.12-0.76%(av.0.53%)na:0.11-0.51%(av.0.36%) Ag:0.48-4.08ppm(av.1.22ppm).Among these elements,the content of Zn,Cu,Cr,Mn,Fe,Al,Mg,Pb and Na increase toward the southwestern area,while the content of Ca and Ag SHOWS the reversed distribution trend.Such a distribution pattern seems to imply that spatial distrivution of heavy metals is closely related to the variation in grain size. X-ray diffractogram show that the minerals in clay from the southwestern mud patch are illite ,chlorite, kaolinte,feldspar and calcite.The bulk of illite in th mud zone is believed to be originated from Huanghe and Yangytze River.The mud patch in this region contains the diagnostic calcite peak,and the concentration of Ca,ni,Pb,Ag are similar to Huanghe type,which indicates that the greater part of these clay fractions may have been derived from the Huanghe River.