• Journal of the Korean Statistical Society
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• v.36 no.2
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• pp.237-256
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• 2007

This paper studies the problem of option pricing in an incomplete market. The market incompleteness comes from the discontinuity of the underlying asset price process which is, in particular, assumed to be a compound Poisson process. To find a reasonable price for a European contingent claim, we first find the unique minimal martingale measure and get a price by taking an expectation of the payoff under this measure. To get a closed-form price, we use an asymptotic expansion. In case where the minimal martingale measure is a signed measure, we use a sequence of martingale measures (probability measures) that converges to the equivalent martingale measure in the limit to compute the price. Again, we get a closed form of asymptotic option price. It is the Black-Scholes price and a correction term, when the distribution of the return process has nonzero skewness up to the first order.

• The Korean Journal of Applied Statistics
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• v.24 no.4
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• pp.721-733
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• 2011

We consider the state price densities that are implicit in financial asset prices. In the pricing of an option, the state price density is proportional to the second derivative of the option pricing function and this relationship together with no arbitrage principle imposes restrictions on the pricing function such as monotonicity and convexity. Since the state price density is a proper density function and most of the shape constraints are caused by this, we propose to estimate the state price density directly by specifying candidate densities in a flexible nonparametric way and applying methods of regularization under extra constraints. The problem is easy to solve and the resulting state price density estimates satisfy all the restrictions required by economic theory.

• Journal of applied mathematics & informatics
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• v.32 no.5_6
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• pp.665-673
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• 2014

Power options have payoffs that are determined by the price of the underlying asset raised to some power. In this paper, power options are considered under a regime-switching model which can capture complex asset dynamics by permitting switching between different regimes. The pricing formulas for the Laplace transforms of power options are obtained. The prices of power options are calculated using the formulas and compared with the results of the Monte Carlo simulation.

• The Pure and Applied Mathematics
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• v.18 no.2
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• pp.129-139
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• 2011

We consider an optimal trading rule in this paper. We assume that the underlying asset follows a mean-reverting process and the transaction consists of one buying and one selling. To maximize the profit, we find price levels to buy low and to sell high. Associated HJB equations are used to formulate the value function. A verification theorem is provided for sufficient conditions. We conclude the paper with a numerical example.

• Proceedings of the Technology Innovation Conference
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• 1999.06a
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• pp.85-97
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• 1999

Being the new paradigm of "knowledge based economy", knowledge asset get to be the key to evaluate the firm's value. For a instance, Scandia firstly informed the intellectual capital report with its own financial statements in 1994. Some financial institutions have emphasized the roles of knowledge assets in the evaluating firm's value, too. But the concept of knowledge asset is so extensively defined that the result of evaluation is not as much reliable as financial statements. As previous studies examined the firm-specific cases, the sectoral pattern of knowledge asset has been ignored and it cause the difficulty in the empirical study. Moreover, the objectivity of study is ambiguous. Therefore, we regards knowledge asset as a technological knowledge asset. Which is related to R&D(research & development) and technology. Because this definition is more measurable than others and can play a frontier role in evaluating the knowledge asset. We extract the criteria related to the technological knowledge asset through the survey of 'Scandia' and other previous studies and add other criteria, which explain the Korean-specific environments. We gather data from "Technological Innovation"(STEPI, 1997, 1999) and "The bibliography of Korean R&D institutes"(KITA,1998) and "the survey of listed company"(Daewoo Securities, 1998. 1999). As the results of empirical study, the variables which explain the financial value of firms do not reflect the 'technological knowledge asset' well. It results from the factors as followings. Firstly, instead of stock price the proxy measurement related to 'knowledge asset' is needed. Secondly, the sample is biased to the large scale firms so we'll collect samples more broadly. Finally, the concept of 'technological knowledge asset' is too narrow to explain the value of firm. We expect the result of this empirical study gives contribution to the evaluation of firms' value more exactly.

• The Journal of Asian Finance, Economics and Business
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• v.7 no.12
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• pp.605-613
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• 2020

In unfrictionless markets, one measure of asset pricing is its height of friction. This study develops a three-factor model by loosening the assumptions about stocks without friction, without risk, and perfectly liquid. Friction is used as an indicator of transaction costs to be included in the model as a variable that will reduce individual profits. This approach is used to estimate return, beta and other variable for firms listed on the Indonesian Stock Exchange (IDX). To test the efficacy of friction-adjusted three-factor model, we use intraday data from July 2016 to October 2018. The sample includes all listed firms; intraday data chosen purposively from regular market are sorted by capitalization, which represents each tick size from the biggest to smallest. We run 3,065,835 intraday data of asking price, bid price, and trading price to get proportional quoted half-spread and proportional effective half-spread. We find evidence of adjusted friction on the three-factor model. High/low trading friction will cause a significant/insignificant return difference before and after adjustment. The difference in average beta that reflects market risk is able to explain the existence of trading friction, while the difference between SMB and HML in all observation periods cannot explain returns and the existence of trading friction.

• Asia-Pacific Journal of Business
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• v.14 no.2
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• pp.51-61
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• 2023

Purpose - Since COVID-19, the government's expansion of liquidity to stimulate the economy has resulted in an increase in private debt and an increase in asset prices of such as real estate and stocks. The recent sharp rise of the US Federal fund rate and tapering by the Fed have led to a fast rise in domestic interest rates, putting a heavy burden on the Korean economy, where the level of household debt is very high. Excessive household debt might have negative effects on the economy, such as shrinking consumption, economic recession, and deepening economic inequality. Therefore, now more than ever, it is necessary to identify the causes of the increase in household debt. Design/methodology/approach - Main methodology is regression analysis. Dependent variable is household loans from depository institutions. Independent variables are consumer price index, unemployment rate, household loan interest rate, housing sales price index, and composite stock price index. The sample periods are from 2017 to May 2022, comprising 72 months of data. The comparative analysis period before and after COVID-19 is from January 2017 to December 2019 for the pre-COVID-19 period, and from Jan 2020 to December 2022 for the post-COVID-19 period. Findings - Looking at the results of the regression analysis for the entire period, it was found that increases in the consumer price index, unemployment rate, and household loan interest rates decrease household loans, while increases in the housing sales price index increase household loans. Research implications or Originality - Household loans of depository institutions are mainly made up of high-credit and high-income borrowers with good repayment ability, so the risk of the financial system is low. As household loans are closely linked to the real estate market, the risk of household loan defaults may increase if real estate prices fall sharply.

• Journal of Intelligence and Information Systems
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• v.25 no.2
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• pp.39-55
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• 2019

Recently banks and large financial institutions have introduced lots of Robo-Advisor products. Robo-Advisor is a Robot to produce the optimal asset allocation portfolio for investors by using the financial engineering algorithms without any human intervention. Since the first introduction in Wall Street in 2008, the market size has grown to 60 billion dollars and is expected to expand to 2,000 billion dollars by 2020. Since Robo-Advisor algorithms suggest asset allocation output to investors, mathematical or statistical asset allocation strategies are applied. Mean variance optimization model developed by Markowitz is the typical asset allocation model. The model is a simple but quite intuitive portfolio strategy. For example, assets are allocated in order to minimize the risk on the portfolio while maximizing the expected return on the portfolio using optimization techniques. Despite its theoretical background, both academics and practitioners find that the standard mean variance optimization portfolio is very sensitive to the expected returns calculated by past price data. Corner solutions are often found to be allocated only to a few assets. The Black-Litterman Optimization model overcomes these problems by choosing a neutral Capital Asset Pricing Model equilibrium point. Implied equilibrium returns of each asset are derived from equilibrium market portfolio through reverse optimization. The Black-Litterman model uses a Bayesian approach to combine the subjective views on the price forecast of one or more assets with implied equilibrium returns, resulting a new estimates of risk and expected returns. These new estimates can produce optimal portfolio by the well-known Markowitz mean-variance optimization algorithm. If the investor does not have any views on his asset classes, the Black-Litterman optimization model produce the same portfolio as the market portfolio. What if the subjective views are incorrect? A survey on reports of stocks performance recommended by securities analysts show very poor results. Therefore the incorrect views combined with implied equilibrium returns may produce very poor portfolio output to the Black-Litterman model users. This paper suggests an objective investor views model based on Support Vector Machines(SVM), which have showed good performance results in stock price forecasting. SVM is a discriminative classifier defined by a separating hyper plane. The linear, radial basis and polynomial kernel functions are used to learn the hyper planes. Input variables for the SVM are returns, standard deviations, Stochastics %K and price parity degree for each asset class. SVM output returns expected stock price movements and their probabilities, which are used as input variables in the intelligent views model. The stock price movements are categorized by three phases; down, neutral and up. The expected stock returns make P matrix and their probability results are used in Q matrix. Implied equilibrium returns vector is combined with the intelligent views matrix, resulting the Black-Litterman optimal portfolio. For comparisons, Markowitz mean-variance optimization model and risk parity model are used. The value weighted market portfolio and equal weighted market portfolio are used as benchmark indexes. We collect the 8 KOSPI 200 sector indexes from January 2008 to December 2018 including 132 monthly index values. Training period is from 2008 to 2015 and testing period is from 2016 to 2018. Our suggested intelligent view model combined with implied equilibrium returns produced the optimal Black-Litterman portfolio. The out of sample period portfolio showed better performance compared with the well-known Markowitz mean-variance optimization portfolio, risk parity portfolio and market portfolio. The total return from 3 year-period Black-Litterman portfolio records 6.4%, which is the highest value. The maximum draw down is -20.8%, which is also the lowest value. Sharpe Ratio shows the highest value, 0.17. It measures the return to risk ratio. Overall, our suggested view model shows the possibility of replacing subjective analysts's views with objective view model for practitioners to apply the Robo-Advisor asset allocation algorithms in the real trading fields.

• The Korean Journal of Applied Statistics
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• v.21 no.5
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• pp.755-763
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• 2008

This paper approaches the problem of option pricing in an incomplete market, where the underlying asset price process follows a compound Poisson model. We assume that the price process follows a compound Poisson model under an equivalent martingale measure and it converges weakly to the Black-Scholes model. First, we express the option price as the expectation of the discounted payoff and expand it at the Black-Scholes price to obtain a pricing formula with three unknown parameters. Then we estimate those parameters using the market option data. This method can use the option data on the same stock with different expiration dates and different strike prices.

• Journal of Information Technology Applications and Management
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• v.29 no.2
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• pp.17-25
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• 2022

Although the two types of currencies compete, the possibility of a virtual currency price bubble is diagnosed by assuming an economic model with currencies (won, virtual currency) that are intrinsically worthless. The won is supplied by the central bank to achieve the price stability target, while the supply of virtual currency increases by a fixed number. According to the basic price theory equation, as a simple proposition, cryptocurrency prices form a Martin Gale process [Schilling and Uhlig, 2019, p.20]. Based on the existing theoretical proposition, we applied the variance ratio verification method [Linton and Smetanina, 2016] and a simple technical chart method for empirical analysis. For the purpose of this study, the possibility of a bubble was empirically analyzed by analyzing the price volatility formed in the Korean virtual currency market over the past year, and brief policy implications for this were presented.