• 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.

• 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.

• 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.

• Communications of the Korean Mathematical Society
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• v.31 no.1
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• pp.199-207
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• 2016

A chained option is a barrier option activated in the event that the underlying asset price crosses barrier or barriers prior to maturity in a specified order. In this paper, we study the pricing of chained options with the quanto property called the "Quanto chained option". A quanto chained option is a chained option starting at time when the foreign exchange rate has the multiple crossing of specified barriers. We provide closed-form formulas for valuing the quanto chained options based on probabilistic approach.

• Journal of applied mathematics & informatics
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• v.38 no.5_6
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• pp.439-461
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• 2020

A step-up option is a newly developed financial instrument that simultaneously provides higher security and profitability. This paper introduces two step-up options: step-up type1 and step-up type2 options, and derives the option pricing formulas using the Laplace transform. We assume that the underlying equity price follows a regime-switching model that reflects the long-term maturity of these options. The option prices are calculated for the two types of funds, a pure stock fund composed of risky assets only and a mixed fund composed of stocks and bonds, to reflect possible variety in the fund underlying asset mix. The impact of changes in the model parameters on the option prices is analyzed. This paper provides information crucial to product developments.

• East Asian mathematical journal
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• v.37 no.1
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• pp.79-85
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• 2021

In this paper, we investigate the valuation of vulnerable exchange option that has credit risk of option issuer. The reduced-form model is used to model credit risk. We assume that credit event is determined by the jump of the counting process with stochastic intensity, which follows the mean reverting process. We propose a simple approach to derive the closed-form pricing formula of vulnerable exchange option under the reduced-form model and provide the pricing formula as the standard normal cumulative function.

• Journal of Korea Technology Innovation Society
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• v.3 no.1
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• pp.37-54
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• 2000

본 글에서는 최근 기술가치평가에 적용되고 있는 조건부가치평가법(Contingent Valuation Method) 다속성효용평가법(Multi-attribute Utility Assessment) 그리고 조건부청구권가치평가법(Real Option Pricing Method)의 세가지 가치측정기법들의 특징과 조요 관련 문헌들을 간략하게 정리하여 소개함으로서 관심있는 연구자들에게 유용한 정보를 제공하고자 한다. 소개하는 방법론들은 환경재화의 가치측정기법과 위험도가 높은 에너지프로젝트의 가치평가기법으로 개발된 기법들로서 신기술이 가지는 특징인 외부성 등의 비시장재적 특성과 높은 위험도에따른 투자가치를 반영할 수있어 기술 및 기업의 가치평가 사례연구에 응용할 수있다.

• 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).

• The Pure and Applied Mathematics
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• v.22 no.3
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• pp.299-313
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• 2015

In this paper, we show the effectiveness of copulas by comparing the correlation of market data of year 2010 with those of years 2006-2009 and investigate copula functions as pricing methods of digital and rainbow options through real market data. We propose an accurate method of pricing rainbow options by using the correlation coefficients obtained from the copula functions depending on strike prices between assetes instead of simple traditional correlation coefficients.

• Kyungpook Mathematical Journal
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• v.62 no.4
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• pp.615-640
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• 2022

In this paper, we investigate a time-dependent double obstacle problem associated with the model of European call option pricing with transaction costs. We prove the existence and uniqueness of a W^2,1_p,loc solution to the problem. We then characterize the behavior of the free boundaries in terms of continuity and values of limit points.