• The Korean Journal of Financial Management
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• v.26 no.3
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• pp.227-246
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• 2009

This study examines the dynamic hedging performances of the Black-Scholes model and Heston model when stock prices drift with stochastic volatilities. Using Monte Carlo simulations, stock prices consistent with Heston's(1993) stochastic volatility option pricing model are generated. In this circumstance, option traders are assumed to use the Black- Scholes model and Heston model to implement dynamic hedging strategies for the options written. The results of simulation indicate that the hedging performance of a mis-specified Black-Scholes model is almost as good as that of a fully specified Heston model. The implication of these results is that the efficacy of the dynamic hedging performances on evaluating the specifications of alternative option models can be limited.

• Communications for Statistical Applications and Methods
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• v.31 no.5
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• pp.585-599
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• 2024

Options pricing remains a critical aspect of finance, dominated by traditional models such as Black-Scholes and binomial tree. However, as market dynamics become more complex, numerical methods such as Monte Carlo simulation are accommodating uncertainty and offering promising alternatives. In this paper, we examine how effective different options pricing methods, from traditional models to machine learning algorithms, are at predicting KOSPI200 option prices and maximizing investment returns. Using a dataset of 2023, we compare the performance of models over different time frames and highlight the strengths and limitations of each model. In particular, we find that machine learning models are not as good at predicting prices as traditional models but are adept at identifying undervalued options and producing significant returns. Our findings challenge existing assumptions about the relationship between forecast accuracy and investment profitability and highlight the potential of advanced methods in exploring dynamic financial environments.

• The Journal of the Korea Contents Association
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• v.13 no.12
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• pp.369-378
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• 2013

The Korean Won-Dollar exchange markets showed radical price movements in the late 1990s and 2008. Therefore it provides good sources for studying volatility phenomena. Using the GARCH option models, I analysed how the prices of foreign exchange options react volatilities in the foreign exchange spot prices. For this I compared the explanatory power of three option models(Black and Scholes, Duan, Heston and Nandi), using the Won-Dollar OTC option markets data from 2006 to 2013. I estimated the parameters using MLE and calculated the mean square pricing errors. According to the my empirical studies, the pricing errors of Duan, Black and Scholes models are 0.1%. And the pricing errors of the Heston and Nandi model is greatest among the three models. So I would like to recommend using Duan or Black and Scholes model for hedging the foreign exchange risks. Finally, the historical average of spot volatilities is about 14%, so trading the options around 5% may lead to serious losses to sellers.

• 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 applied mathematics & informatics
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• v.12 no.1_2
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• pp.335-349
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• 2003

Almost all business are affected by the weather so that weather derivatives has been traded to hedge weather risk. Since the weather itself is not an asset with a market price, some analysts believe that the Black-Scholes equation could not be used appropriately to price weather derivative options. But some weather derivatives can be considered as an Asian option, we revisit the Black-scholes model. Numerical solution of the Black-Scholes equation has a significant error at the money option or around the money option, it is necessary to adopt adaptive mesh near to the strike value. Here we propose a numerical method with an adaptive grid refinement.

• 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 Korea Technology Innovation Society
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• v.8 no.1
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• pp.29-50
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• 2005

Real options provide a new and productive way to view corporate r&d investment decisions. DCF approach is well established and beloved of financial executives, but is known to systematically underestimate investment value under significant uncertainty. Though real options are not inherent in a r&d investment, they can be used to compute the investment value including managerial flexibility like option value. In this paper, we explain how the interval of option value in black-scholes model can be estimated using simulation. We also present a process framework for interval estimation of volatility and efficient of period of investment value. In such a setting, we can obtain the appropriate interval estimation of the expanded investment value.

• Clean Technology
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• v.29 no.1
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• pp.59-70
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• 2023

This study aims to introduce a biowaste processing system that uses spent coffee grounds and implement a real options method to evaluate the proposed process. Energy systems based on eco-friendly fuels lack sufficient data, and thus along with conventional approaches, they lack the techno-economic assessment required for great input qualities. On the other hand, real options analysis can estimate the different costs of options, such as continuing or abandoning a project, by considering uncertainties, which can lead to better decision-making. This study investigated the feasibility of a biowaste processing method using spent coffee grounds to produce biofuel and considered three different valuation models, which were the net present value using discounted cash flow, the Black-Scholes and binomial models. The suggested biowaste processing system consumes 200 kg/h of spent coffee grounds. The system utilizes a tilted-slide pyrolysis reactor integrated with a heat exchanger to warm the air, a combustor to generate a primary heat source, and a series of condensers to harness the biofuel. The result of the net present value is South Korean Won (KRW) -225 million, the result of the binomial model is KRW 172 million, and the result of the Black-Scholes model is KRW 1,301 million. These results reveal that a spent coffee ground-related biowaste processing system is worthy of investment from a real options valuation perspective.

• 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].

• East Asian mathematical journal
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• v.32 no.3
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• pp.301-310
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• 2016

Lookback options, in the terminology of nance, are a type of exotic option with path dependency whose the payoff depends on the optimal (maximum or minimum) underlying asset's price occurring over the life of the option. In this paper, we exploit Mellin transform techniques to find a closed-form solution for European lookback options in Black-Scholes model.