• Journal of the Korean Data and Information Science Society
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• v.25 no.3
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• pp.513-522
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• 2014

Using the assumption that the price of a stock follows a geometric Brownian motion with constant volatility, Black and Scholes (BS) derived a formula that gives the price of a European call option on the stock as a function of the stock price, the strike price, the time to maturity, the risk-free interest rate, the dividend rate paid by the stock, and the volatility of the stock's return. However, implied volatilities of BS method tend to depend on the stock prices and the time to maturity in practice. To address this shortcoming, we estimate the implied volatility function as a function of the strike priceand the time to maturity for data consisting of the daily prices for KOSPI200 call options from January 2007 to May 2009 using support vector regression (SVR), the multiple additive regression trees (MART) algorithm, and ordinary least squaress (OLS) regression. In conclusion, use of MART or SVR in the BS pricing model reduced both RMSE and MAE, compared to the OLS-based BS pricing model.

• Communications for Statistical Applications and Methods
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• v.17 no.2
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• pp.293-308
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• 2010

In this paper, we examine the forecasting KOSPI 200 realized volatility by volatility measurements. The empirical investigation for KOSPI 200 daily returns is done during the period from 3 January 2003 to 29 June 2007. Since Korea Exchange(KRX) will launch VKOSPI futures contract in 2010, forecasting VKOSPI can be an important issue. So we analyze which volatility measurements forecast VKOSPI better. To test this hypothesis, we use 5-minute interval returns to measure realized volatilities. Also, we propose a new methodology that reflects the synchronized bidding and simultaneously takes it account the difference between overnight volatility and intra-daily volatility. The t-test and F-test show that our new realized volatility is not only different from the realized volatility by a conventional method at less than 0.01% significance level, also more stable in summary statistics. We use the correlation analysis, regression analysis, cross validation test to investigate the forecast performance. The empirical result shows that the realized volatility we propose is better than other volatilities, including historical volatility, implied volatility, and convention realized volatility, for forecasting VKOSPI. Also, the regression analysis on the predictive abilities for realized volatility, which is measured by our new methodology and conventional one, shows that VKOSPI is an efficient estimator compared to historical volatility and CRR implied volatility.

• 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.

• Journal of the Korea Academia-Industrial cooperation Society
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• v.12 no.12
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• pp.5671-5676
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• 2011

Volatility Index is the index that represents future volatility of underlying asset implied in option price and expected value of market that measures the possibility of stock price's change expected by investors. The Korea Exchange announces a volatility Index, VKOSPI, since April, 13, 2009. This paper used daily data from January, 2002 through December, 2008 and tested power of Volatility index for future returns of portfolios sorted by size, book-to-market equity and beta. As a result, VKOSPI has the predictive power to future returns and then VKOSPI may be determinants of returns. Also if beta is included when sorting portfolio, the predictive power of VKOSPI is stronger for future portfolio returns.

• Asia-Pacific Journal of Business
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• v.14 no.4
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• pp.319-330
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• 2023

Purpose - The purpose of this paper is to examine the connectedness between categorical economic policy uncertainty (monetary, fiscal, trade and foreign exchange policy uncertainty) indexes and option-implied volatility index in Korea, Japan and the US. Design/methodology/approach - This paper employs the Diebold-Ylmaz (2012) model based on a VAR and generalized forecast error variance decomposition. This paper also conducts regression analyses to investigate whether the volatility indexes are explained by categorical policy uncertainty indexes. Findings - First, we find the total connectedness is stronger in Korea and Japan relative to the US. Second, monetary, fiscal, and foreign exchange policy uncertainty indexes are connected to each other but trade policy uncertainty index is not. Third, the volatility index in Japan and the US is mainly associated with monetary policy uncertainty while the volatility index in Korea is explained by fiscal policy uncertainty index. Research implications or Originality - To our knowledge, this is the first study to investigate the connectedness among categorical policy uncertainty indexes and the volatility index in Korea, Japan, and the US. The empirical results on the connectedness suggest that transparent policy and communication with the market in one type of policy would reduce the uncertainty in other policies.

• The Korean Journal of Applied Statistics
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• v.24 no.1
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• pp.83-92
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• 2011

This paper examines empirically Durham's (2008) asset pricing models to the KOSPI200 index. This model Incorporates the VKOSPI index as a proxy for 1 month integrated volatility. This approach uses option prices to back out implied volatility states with an explicitly speci ed risk-neutral measure and risk premia estimated from the data. The application uses daily observations of the KOSPI200 and VKOSPI indices from January 2, 2003 to September 24, 2010. The empirical results show that non-affine model perform better than affine model.

• Management Science and Financial Engineering
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• v.21 no.2
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• pp.13-23
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• 2015

This study addresses the question as to whether the option prices have useful predictive information on the direction of stock markets by investigating a forecasting power of volatility curvatures and skewness premiums implicit in S&P 500 index option prices traded in Chicago Board Options Exchange. We begin by estimating implied volatility functions and risk neutral price densities every minute based on non-parametric method and then calculate volatility curvature and skewness premium using them. The rationale is that high volatility curvature or high skewness premium often leads to strong bullish sentiment among market participants. We found that the rate of return on the signal following trading strategy was significantly higher than that on the intraday buy-and-hold strategy, which indicates that the S&P500 index option prices have a strong forecasting power on the direction of stock index market. Another major finding is that the information contents of S&P 500 index option prices disappear within one minute, and so one minute-delayed signal following trading strategy would not lead to any excess return compared to a simple buy-and-hold strategy.

• 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].

• Journal for History of Mathematics
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• v.35 no.1
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• pp.1-18
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• 2022

This paper presents a statistical machine learning method that generates the implied volatility surface under the rareness of the market data. We apply the practitioner's Black-Scholes model and Gaussian process regression method to construct a Bayesian inference system with observed volatilities as a prior information and estimate the posterior distribution of the unobserved volatilities. The variance instead of the volatility is the target of the estimation, and the radial basis function is applied to the mean and kernel function of the Gaussian process regression. We present two types of Gaussian process regression methods and empirically analyze them.

• Proceedings of the Korean Operations and Management Science Society Conference
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• 2008.10a
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• pp.263-263
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• 2008