• Journal of the Korean Data and Information Science Society
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• v.24 no.1
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• pp.135-150
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• 2013

This study proposes a novel option strategy by using characteristic of volatility reversion and rough set algorithm in options market. Until now, various research has been conducted on stock and future markets, but minimal research has been done in options market. Particularly, research on the option trading strategy using high frequency data is limited. This study consists of two purposes. The first is to enjoy a profit using volatility reversion model when volatility gap is occurred. The second is to pursue a more stable profit by filtering inaccurate entry point through rough set algorithm. Since options market is affected by various elements like underlying assets, volatility and interest rate, the point of this study is to hedge elements except volatility and enjoy the profit following the volatility gap.

• The Pure and Applied Mathematics
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• v.21 no.4
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• pp.295-305
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• 2014

Yan & Hanson [8] and Makate & Sattayatham [6] extended Bates' model to the stochastic volatility model with jumps in both the stock price and the variance processes. As the solution processes of finding the characteristic function, they sought such a function f satisfying $$f({\ell},{\nu},t;k,T)=exp\;(g({\tau})+{\nu}h({\tau})+ix{\ell})$$. We add the term of order ${\nu}^{1/2}$ to the exponent in the above equation and seek the explicit solution of f.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.20 no.2
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• pp.123-135
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• 2016

This article deals with the pricing of Asian options under a constant elasticity of variance (CEV) model as well as a stochastic elasticity of variance (SEV) model. The CEV and SEV models are underlying asset price models proposed to overcome shortcomings of the constant volatility model. In particular, the SEV model is attractive because it can characterize the feature of volatility in risky situation such as the global financial crisis both quantitatively and qualitatively. We use an asymptotic expansion method to approximate the no-arbitrage price of an arithmetic average Asian option under both CEV and SEV models. Subsequently, the zero and non-zero constant leverage effects as well as stochastic leverage effects are compared with each other. Lastly, we investigate the SEV correction effects to the CEV model for the price of Asian options.

• Journal of Intelligence and Information Systems
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• v.16 no.2
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• pp.19-32
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• 2010

Volatility plays a central role in both academic and practical applications, especially in pricing financial derivative products and trading volatility strategies. This study presents a novel mechanism based on generalized autoregressive conditional heteroskedasticity (GARCH) models that is able to enhance the performance of intelligent volatility trading systems by predicting Korean stock market volatility more accurately. In particular, we embedded the concept of the volatility asymmetry documented widely in the literature into our model. The newly developed Korean stock market volatility index of KOSPI 200, VKOSPI, is used as a volatility proxy. It is the price of a linear portfolio of the KOSPI 200 index options and measures the effect of the expectations of dealers and option traders on stock market volatility for 30 calendar days. The KOSPI 200 index options market started in 1997 and has become the most actively traded market in the world. Its trading volume is more than 10 million contracts a day and records the highest of all the stock index option markets. Therefore, analyzing the VKOSPI has great importance in understanding volatility inherent in option prices and can afford some trading ideas for futures and option dealers. Use of the VKOSPI as volatility proxy avoids statistical estimation problems associated with other measures of volatility since the VKOSPI is model-free expected volatility of market participants calculated directly from the transacted option prices. This study estimates the symmetric and asymmetric GARCH models for the KOSPI 200 index from January 2003 to December 2006 by the maximum likelihood procedure. Asymmetric GARCH models include GJR-GARCH model of Glosten, Jagannathan and Runke, exponential GARCH model of Nelson and power autoregressive conditional heteroskedasticity (ARCH) of Ding, Granger and Engle. Symmetric GARCH model indicates basic GARCH (1, 1). Tomorrow's forecasted value and change direction of stock market volatility are obtained by recursive GARCH specifications from January 2007 to December 2009 and are compared with the VKOSPI. Empirical results indicate that negative unanticipated returns increase volatility more than positive return shocks of equal magnitude decrease volatility, indicating the existence of volatility asymmetry in the Korean stock market. The point value and change direction of tomorrow VKOSPI are estimated and forecasted by GARCH models. Volatility trading system is developed using the forecasted change direction of the VKOSPI, that is, if tomorrow VKOSPI is expected to rise, a long straddle or strangle position is established. A short straddle or strangle position is taken if VKOSPI is expected to fall tomorrow. Total profit is calculated as the cumulative sum of the VKOSPI percentage change. If forecasted direction is correct, the absolute value of the VKOSPI percentage changes is added to trading profit. It is subtracted from the trading profit if forecasted direction is not correct. For the in-sample period, the power ARCH model best fits in a statistical metric, Mean Squared Prediction Error (MSPE), and the exponential GARCH model shows the highest Mean Correct Prediction (MCP). The power ARCH model best fits also for the out-of-sample period and provides the highest probability for the VKOSPI change direction tomorrow. Generally, the power ARCH model shows the best fit for the VKOSPI. All the GARCH models provide trading profits for volatility trading system and the exponential GARCH model shows the best performance, annual profit of 197.56%, during the in-sample period. The GARCH models present trading profits during the out-of-sample period except for the exponential GARCH model. During the out-of-sample period, the power ARCH model shows the largest annual trading profit of 38%. The volatility clustering and asymmetry found in this research are the reflection of volatility non-linearity. This further suggests that combining the asymmetric GARCH models and artificial neural networks can significantly enhance the performance of the suggested volatility trading system, since artificial neural networks have been shown to effectively model nonlinear relationships.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.26 no.4
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• pp.296-309
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• 2022

Timer options are one of the contingent claims that, for given the variance budget, its payoff depends on a random maturity in terms of the realized variance unlike the standard European vanilla option with a fixed time maturity. Since it was first launched by Société Générale Corporate and Investment Banking in 2007, the valuation of the timer options under several stochastic environment for the volatility has been conducted by many researches. In this study, we propose the pricing of timer power options combined with standard timer options and the index of the power to the underlying asset for the investors to actualize lower risks and higher returns at the same time under the uncertain markets. By using the asymptotic analysis, we obtain the first-order approximation of timer power options. Moreover, we demonstrate that our solution has been derived accurately by comparing it with the solution from the Monte-Carlo method. Finally, we analyze the impact of the stochastic volatility with regards to various parameters on the timer power options numerically.

• KDI Journal of Economic Policy
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• v.40 no.4
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• pp.1-22
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• 2018

We estimate three continuous-time stochastic volatility models following the approach by Aït-Sahalia and Kimmel (2007) to compare the Korean and US stock markets. To do this, the Heston, GARCH, and CEV models are applied to the KOSPI 200 and S&P 500 Index. For the latent volatility variable, we generate and use the integrated volatility proxy using the implied volatility of short-dated at-the-money option prices. We conduct MLE in order to estimate the parameters of the stochastic volatility models. To do this we need the transition probability density function (TPDF), but the true TPDF is not available for any of the models in this paper. Therefore, the TPDFs are approximated using the irreducible method introduced in Aït-Sahalia (2008). Among three stochastic volatility models, the Heston model and the CEV model are found to be best for the Korean and US stock markets, respectively. There exist relatively strong leverage effects in both countries. Despite the fact that the long-run mean level of the integrated volatility proxy (IV) was not statistically significant in either market, the speeds of the mean reversion parameters are statistically significant and meaningful in both markets. The IV is found to return to its long-run mean value more rapidly in Korea than in the US. All parameters related to the volatility function of the IV are statistically significant. Although the volatility of the IV is more elastic in the US stock market, the volatility itself is greater in Korea than in the US over the range of the observed IV.

• The Korean Journal of Financial Management
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• v.21 no.2
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• pp.211-233
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• 2004

This purpose of paper is to propose a European option pricing formula when the rate of return follows the leptokurtic distribution instead of normal. This distribution explains well the volatility smile and furthermore the option prices calculated under the leptokurtic distribution are shown to be closer to the market prices than those of Black-Scholes model. We make an estimation of the implied volatility and kurtosis to verify the fitness of the pricing formula that we propose here.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2005.05a
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• pp.753-755
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• 2005

The Black-Scholes (BS) option pricing model is a landmark in contingent claim theory and has found wide acceptance in financial markets. However, it has a difficulty in the use of the model, because the volatility which is a nonlinear function of the other parameters must be estimated. The more accurately investors are able to estimate this value, the more accurate their estimates of theoretical option values will be. This paper proposes a new model which is based on Particle Swarm Optimization (PSO) for finding more precise theoretical values of options in the field of evolutionary computation (EC) than genetic algorithm (GA)or calculus-based search techniques to find estimates of the implied volatility.

• Journal of the Korean Data and Information Science Society
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• v.22 no.3
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• pp.589-596
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• 2011

The conditional autoregressive value at risk (CAViaR) model is useful for risk management, which does not require the assumption that the conditional distribution does not vary over time but the volatility does. But it does not provide volatility forecasts, which are needed for several important applications such as option pricing and portfolio management. For a variety of probability distributions, it is known that there is a constant relationship between the standard deviation and the distance between symmetric quantiles in the tails of the distribution. This inspires us to use a support vector quantile regression (SVQR) for volatility forecasts with the distance between CAViaR forecasts of symmetric quantiles. Simulated example and real example are provided to indicate the usefulness of proposed forecasting method for volatility.

• Korea Trade Review
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• v.41 no.5
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• pp.113-138
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• 2016

This study analyzed the impact when Korea expands Chinese Renminbi(RMB) as invoicing currency on the trade to China using Monte-Carlo simulation. Primarily, we analyzed the impact on the balance of Korean Won(KRW) converted from RMB in a case that simulated exchange rate(Korean won to Chinese Renminbi) and realized historically identical probability distribution but in different stochastic process. In addition, we developed the simulation of the case where the volatility of RMB to KRW exchange rate abnormally expanded. The major results found in this study are as follows. First, in the case where RMB exchange rate simulated in identical probability distribution but in the different stochastic process, no matter how much RMB was utilized as invoicing currency, expansion of the RMB exchange rate and exchange rate volatility operated as positive mechanism to increase the KRW converted balance. Secondly, while the expansion of US dollar exchange rate volatility positively influences the balance on average, it caused a polarization of balance, which makes under-average-balance lower and over-average-balance higher. On the contrary, the expansion of RMB exchange rate volatility even shows a similar mechanism but the impact is more moderate than USD exchange rate volatility. Thirdly, as RMB exchange rate volatility expanded, the balance of translated invoicing currency (RMB) declined, whilst the negative impact of RMB exchange rate volatility on balance of translated invoicing currency(RMB) showed diminishing effect. Lastly, the influence of RMB's exchange rate volatility through RMB usage ratio trends similar to bull spread strategy, which is a combination of call option with put option. Therefore, since RMB usage in invoicing currency could spawn a hedging effect, corporations might utilize RMB as a strategic device for maximizing profits.