• Communications for Statistical Applications and Methods
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• v.17 no.4
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• pp.575-589
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• 2010

Exponential L$\acute{e}$evy models have become popular in modeling price processes recently in mathematical finance. Although it is a relatively simple extension of the geometric Brownian motion, it makes the market incomplete so that the option price is not uniquely determined. As a trial to find an appropriate price for an option, we suppose a situation where a hedger wants to initially invest as little as possible, but wants to have the expected squared loss at the end not exceeding a certain constant. For this, we assume that the underlying price process follows a variance-gamma model and it converges to a geometric Brownian motion as its quadratic variation converges to a constant. In the limit, we use the mean-variance approach to find the asymptotic minimum investment with the expected squared loss bounded. Some numerical results are also provided.

• Science of Emotion and Sensibility
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• v.21 no.4
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• pp.3-10
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• 2018

The present study explores two relationships: first, between number of payment and payment option preference, and second, total sum and payment option preference, with pain of payment as a mediator variable. The analyses revealed that consumers who feel higher pain of payment preferred the pennies-a-day pricing to the aggregate pricing when the per-payment price is low. Consumers who experience higher pain of payment prefer to pay in small frequent installments because they feel the small per-payment price can be comparable to daily expense. Consumers who experienced higher pain of payment preferred aggregate pricing to pennies-a-day pricing when the per-payment price was high. When the per-payment price is high, it is no longer comparable to daily expense, thus leading to greater pain of payment among consumers. The study discusses the implications for mechanism of pain of payment on payment option preference.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.33-50
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• 2023

Foreign exchange options are derivative financial instruments that can exchange one currency for another at a prescribed exchange rate on a specified date. In this study, we examine the analytic formulas for vulnerable foreign exchange options based on multi-scale stochastic volatility driven by two diffusion processes: a fast mean-reverting process and a slow mean-reverting process. In particular, we take advantage of the asymptotic analysis and the technique of the Mellin transform on the partial differential equation (PDE) with respect to the option price, to derive approximated prices that are combined with a leading order price and two correction term prices. To verify the price accuracy of the approximated solutions, we utilize the Monte Carlo method. Furthermore, in the numerical experiments, we investigate the behaviors of the vulnerable foreign exchange options prices in terms of model parameters and the sensitivities of the stochastic volatility factors to the option price.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.597-603
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• 2000

In this paper, we deal with the European Asian Arithmetical option and find the unique rational price associated with option and Asian arithmetical call-put parity.

• Journal of applied mathematics & informatics
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• v.39 no.5_6
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• pp.677-688
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• 2021

In the modern financial market, the scale of financial instrument transactions in the over-the-counter (OTC) market are increasing. However, in this market, there exists a counterparty credit risk. Herein, we obtain a closed-form solution of power option with credit risks, using the double Mellin transforms. We also use a numerical method to compare the differentiations of option price between the closed-form solution and Monte-Carlo simulation. The result shows that the closed-form solution is precise. In addition, the option's price is sensitive to the exponent of the maturity stock price.

• Korean Journal of Construction Engineering and Management
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• v.17 no.1
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• pp.76-82
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• 2016

Decision-making in construction projects often include options features. Such embedded options are difficult to value properly and many decision makers do not have experience in option analysis. The purpose of this paper is to demonstrate how real option analysis can be used to value capital expenditures on construction materials. We propose a real option framework to evaluate decision-making processes involving the purchase of construction materials. A case study was conducted by evaluating the purchase decision-making of solar cells, a good with high price volatility. Using real option analysis two strategies to improve the financial feasibility of installing a solar panel system were derived. The first strategy involves using a price cap that gives the project manager the right, but not obligation, to buy the modules for a predefined price during the next year. The second strategy is to defer the purchase of the solar cells until future price information becomes clearer. Both of the strategies in the case study were valued using the binominal model. This study will help to improve the financial feasibility of purchasing construction materials with high price volatility by including the value of managerial flexibility.

• Journal of the Korean Mathematical Society
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• v.43 no.2
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• pp.383-398
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• 2006

We consider a geometric Levy process for an underlying asset. We prove first that the option price is the unique solution of certain integro-differential equation without assuming differentiability and boundedness of derivatives of the payoff function. Second result is to provide convergence rate for option prices when the small jumps are removed from the Levy process.

• East Asian mathematical journal
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• v.37 no.5
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• pp.553-566
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• 2021

In the over-the-counter market, option's buyers could have a problem for default risk caused by option's writers. In addition, many participants try to maximize their benefits obviously in investing the financial derivatives. Taking all these circumstances into consideration, we deal with the vulnerable power options under a constant elasticity variance (CEV) model. We derive an analytic pricing formula for the vulnerable power option by using the asymptotic analysis, and then we verify that the analytic formula can be obtained accurately by comparing our solution with Monte-Carlo price. Finally, we examine the effect of CEV on the option price based on the derived solution.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.15 no.1
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• pp.31-41
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• 2011

I introduce a derivative called "Snowball Currency Option" or "USDKRWSnowball Extendible At Expiry KO" which was traded once in the over-the-counter market in Korea. A snowball currency option consists of a series of maturities the payoffs at which are like those of a long position in a put option and two short position in an otherwise identical call. The strike price at each maturity depends on the exchange rate and the previous strike price so that the strike prices are random and path-dependent, which makes it difficult to find a closed form solution of the value of a snowball currency option. I analyze the payoff structure of a snowball currency option and derive an upper and a lower boundaries of the value of it in a simplified model. Furthermore, I derive a pricing formula using integral in the simplified model.

• Bulletin of the Korean Mathematical Society
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• v.33 no.2
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• pp.259-265
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• 1996

The history of option valuation problem goes back to the year 1900 when Louis Bachelier deduced on option valuation formula under the assumption that the price process follows standard Brownian motion. More than 50 years later, the research for a mathematical theory of option valuation was taken up by Samuelson ([6]) and others. This work was brought into focus in the major paper by Black and Scholes ([1]) in which a complete option valuation model was derived on the assumption that the underlying price model is a geometric Brownian motion. THis paper starts with subjects developed mainly in Harrison and Kreps ([4]) and in Harrison and Pliska ([5]). The ideas established in these papers are essential for option valuation problem, and in particularfor the point of view that we take in this paper.