• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제27권3호
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• pp.180-193
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• 2023

Approximating the implied volatilities and estimating the model parameters are important topics in quantitative finance. This study proposes an approximation formula for short-maturity near-the-money implied volatilities in stochastic volatility models. A general second-order nonlinear PDE for implied volatility is derived in terms of time-to-maturity and log-moneyness from the Feyman-Kac formula. Using regularity conditions and the Taylor expansion, an approximation formula for implied volatility is obtained for short-maturity nearthe-money call options in two stochastic volatility models: Heston model and SABR model. In addition, we proposed a novel numerical method to estimate model parameters. This method reduces the number of model parameters that should be estimated. Generating sample data on log-moneyness, time-to-maturity, and implied volatility, we estimate the model parameters fitting the sample data in the above two models. Our method provides parameter estimates that are close to true values.

• 자원ㆍ환경경제연구
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• 제11권3호
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• pp.397-414
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• 2002

This paper presents an empirical analysis of exchange rate volatility, petroleum's import price and industrial production on petroleum imports. The GARCH framework is used to measure the exchange rate volatility. One of the most appealing features of the GARCH model is that it captures the volatility clustering phenomenon. We found one long-run relationship between petroleum imports, import price, industrial production, and exchange rate volatility using Johansen's multivariate cointegration methodology. Since there exists a cointegrating vector, therefore, we employ an error correction model to examine the short-run dynamic linkage, finding that the exchange rate volatility performs a key role in the short-run. This paper also apply impulse-response functions to provide the dynamic responses of energy consumption to the exchange rate volatility. The results show that the response of energy consumption to exchange rate volatility declines at the first month and dies out very quickly.

• 품질경영학회지
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• 제41권4호
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• pp.709-724
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• 2013

Purpose: The purpose of this study is to examine five evaluation models constructed by different normalization and aggregation methods in terms of the volatility of rankings and rank reversals. We also explore how the volatility of rankings of the five models changes and how often the rank reversals occur when the outliers are removed. Methods: We used data published in the Complete University Guide 2014. Two universities with missing values were excluded from the data. The university rankings were derived by using the five models, and then each model's volatility of rankings was measured. The box-plot was used to detect outliers. Results: Model 1 has the lowest volatility among the five models whether or not the outliers are included. Model 5 has the lowest number of rank reversals. Model 3, which has been used by many institutions, appears to be in the middle among the five in terms of the volatility and the rank reversals. Conclusion: The university rankings vary from one evaluation model to another depending on what normalization and aggregation methods are used. No single model exhibits clear superiority over others in both the volatility and the rank reversal. The findings of this study are expected to provide a stepping stone toward a superior model which is both reliable and robust.

• Communications for Statistical Applications and Methods
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• 제23권3호
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• pp.203-213
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• 2016

We investigate volatility spillover aspects of realized volatilities (RVs) for the log returns of the Korea Composite Stock Price Index (KOSPI) and the Hang Seng Index (HSI) from 2009-2013. For all RVs, significant long memories and asymmetries are identified. For a model selection, we consider three commonly used time series models as well as three models that incorporate long memory and asymmetry. Taking into account of goodness-of-fit and forecasting ability, Leverage heteroskedastic autoregressive realized volatility (LHAR) model is selected for the given data. The LHAR model finds significant decompositions of the spillover effect from the HSI to the KOSPI into moderate negative daily spillover, positive weekly spillover and positive monthly spillover, and from the KOSPI to the HSI into substantial negative weekly spillover and positive monthly spillover. An interesting result from the analysis is that the daily volatility spillover from the HSI to the KOSPI is significant versus the insignificant daily volatility spillover of the KOSPI to HSI. The daily volatility in Hong Kong affects next day volatility in Korea but the daily volatility in Korea does not affect next day volatility in Hong Kong.

• 디지털융복합연구
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• 제7권1호
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• pp.73-80
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• 2009

In this study, the pricing performances of alternative simple option models are examined by creating a simulated market environment in which asset prices evolve according to a stochastic volatility process. To do this, option prices fully consistent with Heston[9]'s model are generated. Assuming this prices as market prices, the trading positions utilizing the Black-Scholes[4] model, a semi-parametric Corrado-Su[7] model and an ad-hoc modified Black-Scholes model are evaluated with respect to the true option prices obtained from Heston's stochastic volatility model. The simulation results suggest that both the Corrado-Su model and the modified Black-Scholes model perform well in this simulated world substantially reducing the biases of the Black-Scholes model arising from stochastic volatility. Surprisingly, however, the improvements of the modified Black-Scholes model over the Black-Scholes model are much higher than those of the Corrado-Su model.

• The Journal of Asian Finance, Economics and Business
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• 제9권7호
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• pp.1-15
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• 2022

Combining the strength of both Mixed Data Sampling (MIDAS) Regression and realized variance measures, this paper seeks to investigate two objectives: (1) evaluate the post-sample performance of the proposed weekly Realized Variance-MIDAS (RVar-MIDAS) in one-week ahead volatility forecasting against the established Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model and the less explored but robust STES (Smooth Transition Exponential Smoothing) methods. (2) comparing forecast error performance between realized variance and squared residuals measures as a proxy for actual volatility. Data of seven private equity mutual fund indices (generated from 57 individual funds) from two different time periods (with and without financial crisis) are applied to 21 models. Robustness of the post-sample volatility forecasting of all models is validated by the Model Confidence Set (MCS) Procedures and revealed: (1) The weekly RVar-MIDAS model emerged as the best model, outperformed the robust DAILY-STES methods, and the weekly DAILY-GARCH models, particularly during a volatile period. (2) models with realized variance measured in estimation and as a proxy for actual volatility outperformed those using squared residual. This study contributes an empirical approach to one-week ahead volatility forecasting of mutual funds return, which is less explored in past literature on financial volatility forecasting compared to stocks volatility.

• 재무관리논총
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• 제3권1호
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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.

• 자원ㆍ환경경제연구
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• 제22권4호
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• pp.671-689
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• 2013

Transmission mechanisms of volatility between two crude oil markets (WTI and Brent markets) have drawn the attention of numerous academics and practitioners because they both play crucial roles in portfolio and risk management in crude oil markets. In this context, we examined the volatility linkages between two representative crude oil markets using a VECM and an asymmetric bivariate GARCH model. First, looking at the return transmission through the VECM test, we found a long-run equilibrium and bidirectional relationship between two crude oil markets. However, the estimation results of the GARCH-BEKK model suggest that there is unidirectional volatility spillover from the WTI market to the Brent market, implying that the WTI market tends to exert influence over the Brent market and not vice versa. Regarding asymmetric volatility transmission, we also found that bad news volatility in the WTI market increases the volatility of the Brent market. Thus, WTI information is transmitted into the Brent market, indicating that the prices of the WTI market seem to lead the prices of the Brent market.

• 대한수학회논문집
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• 제29권3호
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• pp.489-496
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• 2014

We drive a closed-form expression for the price of a European quanto call option in the double square root stochastic volatility model.

• Journal of the Korean Data and Information Science Society
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• 제22권3호
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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.