• Bulletin of the Korean Mathematical Society
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• v.53 no.5
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• pp.1411-1425
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• 2016

We provide a partial differential equation for European options on a stock whose price process follows a general geometric Riemannian Brownian motion. The existence and the uniqueness of solutions to the partial differential equation are investigated, and then an expression of the value for European options is obtained using the fundamental solution technique. Proper Riemannian metrics on the real number field can make the distribution of return rates of the stock induced by our model have the character of leptokurtosis and fat-tail; in addition, they can also explain option pricing bias and implied volatility smile (skew).

• Proceedings of the Korean Society of Computational and Applied Mathematics Conference
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• 2003.09a
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• pp.10-10
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• 2003

Option pricing theory developed by Black and Sholes depends on an arbitrage opportunity argument. An investor can exactly replicate the returns to any option on that stock by continuously adjusting a portfolio consisting of a stock and a riskless bond. The value of the option equal the value of the replicating portfolio. However, transactions costs invalidate the Black-Sholes arbitrage argument for option pricing, since continuous revision implies infinite trading, Discrete revision using Black-Sholes deltas generates errors which are correlated with the market, and do not approach zero with more frequent revision when transactions costs are included. Stochastic calculus serves as a fundamental tool in the mathematical finance. We closely look at the utility maximization theory which is one of the main option valuation methods. We also see that how the stochastic optimal control problems and their solution methods are applied to the theory.

• KDI Journal of Economic Policy
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• v.33 no.2
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• pp.41-79
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• 2011

This study examines the compensation scheme for the executives and risk-taking behavior in the Korean banks. Theoretically, shareholders prefer risky asset choice to the optimal one due to the limited liability feature of reward, and stock-based executive compensation may induce choices favorable to the shareholder. We empirically test this risk-taking hypothesis using Korean banks' data. Since only the stock option data is available under the current disclosure system, we limit our analysis to examine the relationship between the compensation through stock option and the risk of banks. The result provides no evidence that stock option compensations increase the risk of banks, which is contrary to the theoretical prediction and preceding studies in the US. This may be due to any factor that the executive reward data omit, or regulation effects on the bank management.

• The Korean Journal of Financial Management
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• v.1 no.1
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• pp.133-149
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• 1985

The theory of option pricing has undergone rapid advances in recent years. Simultaneously, organized option markets have developed in the United States and Europe. The closed form solution for pricing options has only recently been developed, but its potential for application to problems in finance is tremendous. Almost all financial assets are really contingent claims. Especially, Black and Scholes(1973) suggest that the equity in a levered firm can be thought of as a call option. When shareholders issue bonds, it is equivalent to selling the assets of the firm to the bond holders in return for cash (the proceeds of the bond issues) and a call option. This paper takes the insight provided by Black and Scholes and shows how it may be applied to many of the traditional issues in corporate finance such as dividend policy, acquisitions and divestitures and capital structure. In this paper a combined capital asset pricing model (CAPM) and option pricing model (OPM) is considered and then applied to the derivation of equity value and its systematic risk. Essentially, this paper is an attempt to gain a clearer focus theoretically on the question of corporate stock risk and how the OPM adds to its understanding.

• Korean Management Science Review
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• v.27 no.3
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• pp.33-41
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• 2010

A lot of researches find negative volatility risk premium in options market. We can make a trading profit by exploiting the negative volatility premium. This study proposes negative volatility risk premium hypotheses in the KOSPI 200 stock price index options market and empirically test the proposed hypotheses with intra-day short straddle strategy. This strategy sells both at-the-money call option and at-the-money put option at market open and exits the position at market close. Using MySQL 5.1, we create our database with 1 minute option price data of the KOSPI 200 index options from 2004 to 2009. Empirical results show that negative volatility risk premium exists in the KOSPI 200 stock price index options market. Furthermore, intra-day short straddle strategy consistently produces annual profits except one year.

• Management Science and Financial Engineering
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• v.21 no.2
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• pp.13-23
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• 2015

This study addresses the question as to whether the option prices have useful predictive information on the direction of stock markets by investigating a forecasting power of volatility curvatures and skewness premiums implicit in S&P 500 index option prices traded in Chicago Board Options Exchange. We begin by estimating implied volatility functions and risk neutral price densities every minute based on non-parametric method and then calculate volatility curvature and skewness premium using them. The rationale is that high volatility curvature or high skewness premium often leads to strong bullish sentiment among market participants. We found that the rate of return on the signal following trading strategy was significantly higher than that on the intraday buy-and-hold strategy, which indicates that the S&P500 index option prices have a strong forecasting power on the direction of stock index market. Another major finding is that the information contents of S&P 500 index option prices disappear within one minute, and so one minute-delayed signal following trading strategy would not lead to any excess return compared to a simple buy-and-hold strategy.

• Journal of the Korean Data and Information Science Society
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• v.20 no.6
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• pp.1061-1073
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• 2009

Stock price index option investing is a scientific investment method and various index and investment strategies have been developed. The purpose of this study is to apply the variety of option investment strategies that have been introduced in the market and validate them using past option trading data. Option data was based on an actual stock exchange market tick data ranging from September 2001 to January 2007. Visual Basic is used to propose an option back-testing model. Validation process was carried out by transferring the tick data into ten-minute intervals and empirically analyzed. Furthermore, most option-related strategies have been applied to the model, and the usefulness of each strategies can be easily evaluated. As option investment has high leverage followed by high risks and profit, the optimal option investment strategy should be used according to the market condition at the time to make stable profit with minimum risk.

• 한국벤처창업학회:학술대회논문집
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• 2023.04a
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• pp.45-50
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• 2023

본 논문은 스타트업과 벤처기업의 임직원이 상장후 적법한 절차에 따라 스톡옵션 행사를 하였지만, 주식시장의 주가에 악영향을 미치며 일반투자자 피해가 발생하여 도덕적 해이 논란이 촉발되었고 이 문제에 대해 정부 규제당국이 직접적인 추가규제를 예정하고 있는 상황에서 주식매수선택권제도(Stock Option, 이하 스톡옵션)의 보완 수단인 양도제한조건부주식(Restricted Stock Unit, 이하 RSU)제도를 도입함으로써 시장중심적으로 이 문제를 풀어내는 선진 스타트업 벤처금융 방안을 제시하는 것이 목적이다. 이를 위해, 본 논문은 첫째, RSU의 개념에 대해 제한조건부주식(Restricted Stock, 이하 RS)와 비교논의를 통해 제시하며. RSU의 스톡옵션에 대한 보완적 특징 설명에서는 기존 스톡옵션제도와 RSU를 비교 설명하였다. 둘째, RSU의 단점과 한계점을 설명하고 그 한계점을 극복하며 국내 스타트업과 벤처기업들이 이를 효과적으로 도입 할 수 있는 방안을 제시하였다. 셋째, RSU의 도입 현황을 제시하며 향후 RSU 도입 위한 정책방안들을 제안하였다. 본 논문은 이를 통해 RSU가 기본 스톡옵션제도의 규제강화를 통한 시장 위축적인 해결보다는, 새로운 대안을 주식연계형 보상방안 대안을 제시함으로써 보다 시장친화적인 제도를 마련함으로써 국내 스타트업과 벤처기업의 인력수급 해소와 사업활성화에 큰 의미를 벤처생태계 스스로가 풀어내는데에 기여할 것으로 기대한다.

• Journal of the Korean Data and Information Science Society
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• v.25 no.3
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• pp.513-522
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• 2014

Using the assumption that the price of a stock follows a geometric Brownian motion with constant volatility, Black and Scholes (BS) derived a formula that gives the price of a European call option on the stock as a function of the stock price, the strike price, the time to maturity, the risk-free interest rate, the dividend rate paid by the stock, and the volatility of the stock's return. However, implied volatilities of BS method tend to depend on the stock prices and the time to maturity in practice. To address this shortcoming, we estimate the implied volatility function as a function of the strike priceand the time to maturity for data consisting of the daily prices for KOSPI200 call options from January 2007 to May 2009 using support vector regression (SVR), the multiple additive regression trees (MART) algorithm, and ordinary least squaress (OLS) regression. In conclusion, use of MART or SVR in the BS pricing model reduced both RMSE and MAE, compared to the OLS-based BS pricing model.

• Communications of the Korean Mathematical Society
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• v.23 no.1
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• pp.141-151
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• 2008

In this paper, we derive the nonlinear equation for European option pricing containing liquidity risk which can be defined as the inverse of the partial derivative of the underlying asset price with respect to the amount of assets traded in the efficient market. Numerical solutions are obtained by using finite element method and compared with option prices of KOSPI200 Stock Index. These prices computed with liquidity risk are considered more realistic than the prices of Black-Scholes model without liquidity risk.