• Journal of the Korean Mathematical Society
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• v.43 no.4
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• pp.845-858
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• 2006

We present two approaches of the stochastic interest rate European option pricing model. One is a bond numeraire approach which is applicable to a nonzero value asset. In this approach, we assume log-normality of returns of the asset normalized by a bond whose maturity is the same as the expiration date of an option instead that of an asset itself. Another one is the expectation hypothesis approach for value zero asset which has futures-style margining. Bond numeraire approach allows us to calculate volatilities implied in options even though stochastic interest rate is considered.

• New & Renewable Energy
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• v.10 no.1
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• pp.41-49
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• 2014

For a proper valuation of wind power project, it is necessary to consider volatilities of key parameters such as annual energy production, electricity sales price, and long term interest rate. Real option methodology allows to calculate option values of these parameters. Volatilities to be considered in wind project valuation are 1) annual energy production (AEP) estimation due to meteorological variation and estimation errors in wind speed distribution, 2) changes in system marginal price (SMP), and 3) interest rate fluctuation of project financing which provides refinancing option to be exercised during a loan tenor for commercial scale projects. Real option valuation turns out to be more than half of the sales value based on a case study for a FIT scheme wind project that was sold to a financial investor.

• Communications of the Korean Mathematical Society
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• v.31 no.2
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• pp.415-422
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• 2016

We derive a closed-form expression for the price of a European quanto call option when both foreign and domestic interest rates follow the Vasicek's short rate model.

• Korean Journal of Mathematics
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• v.23 no.1
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• pp.81-91
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• 2015

This paper is about the local volatility for the price of a European quanto call option. We derive the explicit formula of the local volatility with constant foreign and domestic interest rates by adapting the methods of Dupire and Derman & Kani. Furthermore, we obtain the Dupire equation for the local volatility with stochastic interest rates.

• Communications of the Korean Mathematical Society
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• v.33 no.1
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• pp.345-360
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• 2018

In finance, barrier options are options contracts with a payoff that depends on whether the price of the underlying asset hits a predetermined barrier level during the option's lifetime. Based on exotic options and random fluctuations of interest rates in the marketplace, we consider discount barrier options with a stochastic interest rate driven by the Hull-White process. This paper derives the closed-form solutions of the discount barrier option and the discount double barrier option using Mellin transform methods and the PDE (partial differential equation) method of images.

• Communications of the Korean Mathematical Society
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• v.32 no.2
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• pp.467-477
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• 2017

This paper is about the derivations of local volatilities for European quanto call option prices according to various types of payoffs. We derive the explicit formulas of local volatilities with constant foreign and domestic interest rates by adapting the method of Derman-Kani.

• Journal of Korea Society of Digital Industry and Information Management
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• v.6 no.3
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• pp.211-219
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• 2010

This paper designs the dynamic symbol automatic trading system in Korean option market. This system is based on Multichart program which is convenient and efficient system trading tool. But the Multichart has an important restriction which has only one constant symbol per chart. This restriction causes very useful strategies impossible. The proposed design uses global variables, signal chart selection and position order exchange. So an automatic trading system with dynamic symbol works on Multichart program. To verify the proposed system, BS(Buythensell)-SB(Sellthenbuy) strategies are tested which uses the change of open-interest of stock index futures within a day. These strategies buy both call and put option in ATM at start candle and liquidate all at 12 o'clock and then sell both call and put option in ATM at 12 o'clock and also liquidate all at 14:40. From 23 March 2009 to 31 May 2010, 301-trading days, is adopted for experiment. As a result, the average daily profit rate of this simple strategies riches 1.09%. This profit rate is up to eight times of commision price which is 0.15 % per option trade. If the method which raises the profitable rate of wining trade or lower commission than 0.15% is found, these strategies make fascinated lossless trading system which is based on the proposed dynamic symbol automatic trading system.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.22 no.49
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• pp.43-57
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• 1999

The recent trend is that risk management has more and more its importance. Neverthless, Korea's risk management is not developed. Even most banks does gap, duration in ALM for risk management, development and operation of VaR stressed at BIS have elementary level. In the case of Fallon and Pritsker, Marshall, gamma model is superior to delta model and Monte Carlo Simulation is improved at its result, as sample number is increased. And, nonparametric model is superior to parametric model. In the case of Korea's stock portfolio, VaR of Monte Carlo Simulation and Full Variance Covariance Model is less than that of Diagonal Model. The reason is that VaR of Full Variance Covariance Model is more precise than that of Diagonal Model. By the way, in the case of interest rate, result of monte carlo simulation is less than that of delta-gamma analysis on 95% confidence level. But, result of 99% is reversed. Therefore, result of which method is not dominated. It means two fact at forecast on volatility of stock and interest rate portfolio. First, in Delta-gamma method and Monte Carlo Simulation, assumption of distribution affects Value at Risk. Second, Value at Risk depends on test method. And, if option price is included, test results will have difference between the two. Therefore, If interest rate futures and option market is open, Korea's findings is supposed to like results of other advanced countries. And, every banks try to develop its internal model.

• Journal of the Korean Data and Information Science Society
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• v.24 no.4
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• pp.737-753
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• 2013

Interest rate options embedded in life insurance products provide policyholders with minimum guaranteed rates credited to the corresponding surrender values. This paper discusses current low-interest environment and several types of interest rate options embedded in life insurance products. In addition, this paper shows profit structures of the life insurance products and calculates values of the interest rate options under stochastic interest model and the corresponding VaR (value at risk). Finally, some implications are discussed.

• Asia-Pacific Journal of Business
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• v.12 no.3
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• pp.379-396
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• 2021

Purpose - The purpose of this paper is to study the rational payoff from the standpoint of foreign investors and the government when the government issues GDP-linked bonds to foreign investors. Design/methodology/approach - In this paper, the prices of 12 types of GDP-linked bond structures, which are classified according to the calculation cycle of the rate of change of linked GDP, the currency issued, and whether options are embedded, were evaluated. The Fama-French 3-factor model and the GMM-SDF model are used in the asset pricing model, and domestic and overseas investors used different basis assets. Findings - The KRW premium for US investors is estimated to be 43bp on a quarterly basis and 30bp on an annual basis, respectively, meaning that when the government issues bonds in KRW, the interest rate paid to US investors will be reduced by 30bp to 160bp (annually converted). Using the Fama-French 3 factor model, the KRW premium is the risk premium for the US market beta, meaning that if US investors do not intend to invest in US market beta, it is advantageous to receive an additional interest rate by investing in USD-denominated GDP-linked bonds. Korea's GDP- linked bond give US investors diversified investment utility, so they are willing to incorporate Korean GDP-linked bonds even if -150bp of interest is deducted from the structure issued to Korean investors. And as a result of estimating the value of the option through the GDP-linked bond with options that provides a floor for guaranteeing the principal, the value of the option linked to the annual GDP issued in dollars was the lowest. Research implications or Originality - Issuing dollar-denominated GDP-linked bonds linked to annual GDP with the option of guaranteeing the principal by the government is a way to increase investment opportunities for US investors and achieve financial stability of the government.