• The Korean Journal of Applied Statistics
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• v.25 no.1
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• pp.55-66
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• 2012

Option pricing models using L$\acute{e}$evy processes are suggested as an alternative to the Black-Scholes model since empirical studies showed that the Black-Sholes model could not reflect the movement of underlying assets. In this paper, we investigate whether the Variance Gamma model can reflect the movement of underlying assets in the Korean stock market better than the Black-Scholes model. For this purpose, we estimate parameters and perform likelihood ratio tests using KOSPI 200 data based on the density for the log return and the option pricing formula proposed in Madan et al. (1998). We also calculate some statistics to compare the models and examine if the volatility smile is corrected through regression analysis. The results show that the option price estimated under the Variance Gamma process is closer to the market price than the Black-Scholes price; however, the Variance Gamma model still cannot solve the volatility smile phenomenon.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.769-784
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• 2013

We consider the modulus-based successive overrelaxation method for the linear complementarity problems from the discretization of Black-Scholes American options model. The $H_+$-matrix property of the system matrix discretized from American option pricing which guarantees the convergence of the proposed method for the linear complementarity problem is analyzed. Numerical experiments confirm the theoretical analysis, and further show that the modulus-based successive overrelaxation method is superior to the classical projected successive overrelaxation method with optimal parameter.

• Journal of Korean Society of Industrial and Systems Engineering
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• v.45 no.4
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• pp.21-30
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• 2022

To mitigate the environmental impacts of the energy sector, the government of South Korea has made a continuous effort to facilitate the development and commercialization of renewable energy. As a result, the efficiency of renewable energy plants is not a consideration in the potential site selection process. To contribute to the overall sustainability of this increasingly important sector, this study utilizes the Black-Scholes model to evaluate the economic value of potential sites for off-site wind farms, while analyzing the environmental mitigation of these potential sites in terms of carbon emission reduction. In order to incorporate the importance of flexibility and uncertainty factors in the evaluation process, this study has developed a site evaluation model focused on system dynamics and real option approaches that compares the expected revenue and expected cost during the life cycle of off-site wind farm sites. Using sensitivity analysis, this study further investigates two uncertainty factors (namely, investment cost and wind energy production) on the economic value and carbon emission reduction of potential wind farm locations.

• Bulletin of the Korean Mathematical Society
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• v.51 no.4
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• pp.1087-1100
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• 2014

We present an accurate and efficient numerical method for solving the Black-Scholes equation. The method uses an adaptive grid technique which is based on a far-field boundary position and the Peclet condition. We present the algorithm for the automatic adaptive grid generation: First, we determine a priori suitable far-field boundary location using the mathematical model parameters. Second, generate the uniform fine grid around the non-smooth point of the payoff and a non-uniform grid in the remaining regions. Numerical tests are presented to demonstrate the accuracy and efficiency of the proposed method. The results show that the computational time is reduced substantially with the accuracy being maintained.

• The Pure and Applied Mathematics
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• v.27 no.1
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• pp.43-50
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• 2020

We investigate the domain of influence of the local volatility function on the solutions of the general Black-Scholes model. First, we generate the sample paths of underlying asset using the Monte Carlo simulation. Next, we define the inner and outer domains to find the effective volatility region. To confirm the effect of the inner domain, we use the root mean square error for the European call option prices, and then change the values of volatility in the proposed domain. The computational experiments confirm that there is an effective region which dominates the option pricing.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.2
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• pp.121-137
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• 2022

In this paper, we investigate an efficient hybrid method for solving two-asset time fractional Black-Scholes partial differential equations. The proposed method is based on the Crank-Nicolson the radial basis functions methods. We show that, this method is convergent and we obtain good approximations for solution of our problems. The numerical results show high accuracy of the proposed method without needing high computational cost.

• Communications for Statistical Applications and Methods
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• v.14 no.2
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• pp.459-479
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• 2007

Theories related to financial market has received big attention from the statistics community. However, not many courses on the topic are provided in statistics departments. Because the financial theories are entangled with many complicated mathematical and physical theories as well as ambiguously stated financial terminologies. Based on our experience on the topic, we try to explain the rather complicated terminologies and theories with easy-to-understand words. This paper will briefly cover the topics of basic terminologies of derivatives, Black-Scholes pricing idea, and related basic mathematical terminologies.

• Journal of applied mathematics & informatics
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• v.2 no.2
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• pp.47-52
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• 1995

in this paper we reduce the trading strategy of discounted security model to trading strategy of original model

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.14 no.4
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• pp.249-273
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• 2010

Often in practice, the implied volatility of an option is calculated to find the option price tomorrow or the prices of, nearby' options. To show that one does not need to adhere to the Black- Scholes formula in this scheme, Figlewski has provided a new pricing formula and has shown that his, alternating passive model' performs as well as the Black-Scholes formula [8]. The Figlewski model was modified by Henderson et al. so that the formula would have no static arbitrage [10]. In this paper, we show how to construct a huge class of such static no arbitrage pricing functions, making use of distortions, coherent risk measures and the pricing theory in incomplete markets by Carr et al. [4]. Through this construction, we provide a more elaborate static no arbitrage pricing formula than Black-Sholes in the above scheme. Moreover, using our pricing formula, we find a volatility curve which fits with striking accuracy the synthetic data used by Henderson et al. [10].

• The Korean Journal of Financial Studies
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• v.3 no.1
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• pp.213-231
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• 1996

In this study we conduct a specification test of at-the-money option volatility. Results show that the implied volatility estimate recovered from the Black-Scholes European option pricing model is nearly indistinguishable from the implied volatility estimate obtained from the Barone-Adesi and Whaley's American option pricing model. This study also investigates whether the use of Black-Scholes implied volatility estimates in American put pricing model significantly affect the prediction the prediction of American put option prices. Results show that, at long as the possibility of early exercise is carefully controlled in calculation of implied volatilities prediction of American put prices is not significantly distorted. This suggests that at-the-money option implied volatility estimates are robust across option pricing model.