• Title/Summary/Keyword: Mean Reverting Process

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분산성(分散性) 변화(變化)가 주가(株價)에 미치는 영향(影響)과 분산성(分散性)의 평균회귀속도(平均回歸速度)에 관한 실증적(實證的) 연구(硏究)

  • Lee, Sang-Bin;Ok, Gi-Yul
    • The Korean Journal of Financial Management
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    • v.9 no.1
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    • pp.111-133
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    • 1992
  • 본 연구는 미국과 일본의 주식시장(株式市場)을 연구대상으로 하여 주식시장에서의 분산성(分散性) 변화(變化)의 시점(時點)을 찾고 이 분산성 변화가 주가(株價)에 미치는 영향(影響)과 분산성의 평균회귀속도(平均回歸速度)에 대해 실증적으로 살펴보았다. 분산성(分散性)의 비교구간을 월 단위, 주 단위 및 하루 단위로 하여 분산성(分散性)이 변화(變化)한 시점을 찾고 이 변화 시점을 기준으로 하여 각 단위구간(單位區間)에서의 분산성(分散性) 변화(變化)에 대한 주가(株價)의 반응을 분석하였다. 또한 각 단위구간별로 분산성(分散性)이 변화(變化)한 시점(時點)이후로 이 분산성 변화 블럭 다음의 블럭에 대한 투자자의 반응도 살펴봄으로써 분산성(分散性) 변화(變化)의 평균회귀과정(平均回歸過程)(mean-reverting process) 및 평균으로의 회귀가 얼마나 빨리 되는가의 여부를 알아보았다. 분산성(分散性) 증가(增加)나 분산성(分散性) 감소(減少)와 같은 분산성 변화가 주가(株價)에 미치는 영향은 분산성(分散性) 비교 구간의 장단기(長短期)에 따라 다른 결과를 보였다.

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PRICING AMERICAN LOOKBACK OPTIONS UNDER A STOCHASTIC VOLATILITY MODEL

  • Donghyun Kim;Junhui Woo;Ji-Hun Yoon
    • Bulletin of the Korean Mathematical Society
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    • v.60 no.2
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    • pp.361-388
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    • 2023
  • In this study, we deal with American lookback option prices on dividend-paying assets under a stochastic volatility (SV) model. By using the asymptotic analysis introduced by Fouque et al. [17] and the Laplace-Carson transform (LCT), we derive the explicit formula for the option prices and the free boundary values with a finite expiration whose volatility is driven by a fast mean-reverting Ornstein-Uhlenbeck process. In addition, we examine the numerical implications of the SV on the American lookback option with respect to the model parameters and verify that the obtained explicit analytical option price has been obtained accurately and efficiently in comparison with the price obtained from the Monte-Carlo simulation.

PRICING OF TIMER DIGITAL POWER OPTIONS BASED ON STOCHSTIC VOLATILITY

  • Mijin Ha;Sangmin Park;Donghyun Kim;Ji-Hun Yoon
    • East Asian mathematical journal
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    • v.40 no.1
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    • pp.63-74
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    • 2024
  • Timer options are financial instruments proposed by Société Générale Corporate and Investment Banking in 2007. Unlike vanilla options, where the expiry date is fixed, the expiry date of timer options is determined by the investor's choice, which is in linked to a variance budget. In this study, we derive a pricing formula for hybrid options that combine timer options, digital options, and power options, considering an environment where volatility of an underlying asset follows a fast-mean-reverting process. Additionally, we aim to validate the pricing accuracy of these analytical formulas by comparing them with the results obtained from Monte Carlo simulations. Finally, we conduct numerical studies on these options to analyze the impact of stochastic volatility on option's price with respect to various model parameters.

Capital Structure's Mean-Reversion and Long-Term Equilibrium (자본구조의 평균회귀현상과 장기균형)

  • Son, Pan-Do;Son, Seung-Tae
    • The Korean Journal of Financial Management
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    • v.25 no.3
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    • pp.33-78
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    • 2008
  • This paper empirically examines whether firms engage in a dynamic adjustment process toward target capital structure and, whether there is a target capital structure or mean reverting using the partial adjustment model while allowing for costly adjustment. Also we investigate the empirical determinants of optimal target capital structure in long term equilibrium. As a result, our empirical model captures at least several important features of capital structure behavior for Korean listed firms. First, Korean firms pursue target capital structure and also there is mean reverting phenomenon. Second, Non-Chaebol and small firm in adjustment speed is faster than Chaebol and large firm. Third, even capital market restricts the adjustment speed interestingly. Fourth, Korean firms have target behavior according to a degree of observed gap. Fifth, Korean firms close about one-fourth of the gap between their actual and target debt ratios within one year and thence targeting behavior explains far more of the observed changes in capital structure than market timing or pecking order considerations. Sixth, capital market is significant in determining optimal capital structure.

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Real Option Analysis for Medium-scale CHP Plant Investment with Volatile Electricity Prices (실물옵션을 이용한 소형열병합발전의 경제성 평가 : 전력가격 변동성을 고려하여)

  • Park, Hojeong;Jang, Chulho
    • Environmental and Resource Economics Review
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    • v.16 no.4
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    • pp.763-779
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    • 2007
  • The combined heat-and-power (CHP) plant is recently suggested as an effective resolution in response to recent rising oil prices and the Kyoto Protocol. This research provides a model for economic appraisal to evaluate CHP investment. Real option model is developed to incorporate a case where the investment is irreversible and underlying revenue is stochastic. The analysis shows that power plant capacity more than 40 Gcal makes CHP investment profitable while the results may vary 10 modest level with respect to investment cost, heat sales price and discount rate.

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A Study on Properties of Crude Oil Based Derivative Linked Security (유가 연계 파생결합증권의 특성에 대한 연구)

  • Sohn, Kyoung-Woo;Chung, Ji-Yeong
    • Asia-Pacific Journal of Business
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    • v.11 no.3
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    • pp.243-260
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    • 2020
  • Purpose - This paper aims to investigate the properties of crude oil based derivative security (DLS) focusing on step-down type for comprehensive understanding of its risk. Design/methodology/approach - Kernel estimation is conducted to figure out statistical feature of the process of oil price. We simulate oil price paths based on kernel estimation results and derive probabilities of hitting the barrier and early redemption. Findings - The amount of issuance for crude oil based DLS is relatively low when base prices are below $40 while it is high when base prices are around $60 or $100, which is not consistent with kernel estimation results showing that oil futures prices tend to revert toward $46.14 and the mean-reverting speed is faster as oil price is lower. The analysis based on simulated oil price paths reveals that probability of early redemption is below 50% for DLS with high base prices and the ratio of the probability of early redemption to the probability of hitting barrier is remarkably low compared to the case for DLS with low base prices, as the chance of early redemption is deferred. Research implications or Originality - Empirical results imply that the level of the base price is a crucial factor of the risk for DLS, thus introducing a time-varying knock-in barrier, which is similar to adjust the base price, merits consideration to enhance protection for DLS investors.

A Data-based Sales Forecasting Support System for New Businesses (데이터기반의 신규 사업 매출추정방법 연구: 지능형 사업평가 시스템을 중심으로)

  • Jun, Seung-Pyo;Sung, Tae-Eung;Choi, San
    • Journal of Intelligence and Information Systems
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    • v.23 no.1
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    • pp.1-22
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    • 2017
  • Analysis of future business or investment opportunities, such as business feasibility analysis and company or technology valuation, necessitate objective estimation on the relevant market and expected sales. While there are various ways to classify the estimation methods of these new sales or market size, they can be broadly divided into top-down and bottom-up approaches by benchmark references. Both methods, however, require a lot of resources and time. Therefore, we propose a data-based intelligent demand forecasting system to support evaluation of new business. This study focuses on analogical forecasting, one of the traditional quantitative forecasting methods, to develop sales forecasting intelligence systems for new businesses. Instead of simply estimating sales for a few years, we hereby propose a method of estimating the sales of new businesses by using the initial sales and the sales growth rate of similar companies. To demonstrate the appropriateness of this method, it is examined whether the sales performance of recently established companies in the same industry category in Korea can be utilized as a reference variable for the analogical forecasting. In this study, we examined whether the phenomenon of "mean reversion" was observed in the sales of start-up companies in order to identify errors in estimating sales of new businesses based on industry sales growth rate and whether the differences in business environment resulting from the different timing of business launch affects growth rate. We also conducted analyses of variance (ANOVA) and latent growth model (LGM) to identify differences in sales growth rates by industry category. Based on the results, we proposed industry-specific range and linear forecasting models. This study analyzed the sales of only 150,000 start-up companies in Korea in the last 10 years, and identified that the average growth rate of start-ups in Korea is higher than the industry average in the first few years, but it shortly shows the phenomenon of mean-reversion. In addition, although the start-up founding juncture affects the sales growth rate, it is not high significantly and the sales growth rate can be different according to the industry classification. Utilizing both this phenomenon and the performance of start-up companies in relevant industries, we have proposed two models of new business sales based on the sales growth rate. The method proposed in this study makes it possible to objectively and quickly estimate the sales of new business by industry, and it is expected to provide reference information to judge whether sales estimated by other methods (top-down/bottom-up approach) pass the bounds from ordinary cases in relevant industry. In particular, the results of this study can be practically used as useful reference information for business feasibility analysis or technical valuation for entering new business. When using the existing top-down method, it can be used to set the range of market size or market share. As well, when using the bottom-up method, the estimation period may be set in accordance of the mean reverting period information for the growth rate. The two models proposed in this study will enable rapid and objective sales estimation of new businesses, and are expected to improve the efficiency of business feasibility analysis and technology valuation process by developing intelligent information system. In academic perspectives, it is a very important discovery that the phenomenon of 'mean reversion' is found among start-up companies out of general small-and-medium enterprises (SMEs) as well as stable companies such as listed companies. In particular, there exists the significance of this study in that over the large-scale data the mean reverting phenomenon of the start-up firms' sales growth rate is different from that of the listed companies, and that there is a difference in each industry. If a linear model, which is useful for estimating the sales of a specific company, is highly likely to be utilized in practical aspects, it can be explained that the range model, which can be used for the estimation method of the sales of the unspecified firms, is highly likely to be used in political aspects. It implies that when analyzing the business activities and performance of a specific industry group or enterprise group there is political usability in that the range model enables to provide references and compare them by data based start-up sales forecasting system.