• Korean Journal of Mathematics
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• v.20 no.1
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• pp.47-60
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• 2012

We deal some analytic calculations for European option pricing by using the theory of elementary solution of generalized diffusion equation mainly.

• Economic Analysis
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• v.25 no.3
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• pp.70-99
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• 2019

Using a stochastic volatility-in-mean VAR model consisting of the KOSPI index, the foreign exchange rate, the government bond rate, and the credit spread, this study investigates the effects of financial market uncertainty on financial markets. We find that higher uncertainty has recessionary effects on financial markets. The effects are especially stronger in equity markets and in won-dollar exchange markets. We also find that the effects of uncertainty become stronger during times of financial market stress compared to normal times. Finally, the results imply that financial market uncertainty may potentially affect the real sector, too.

• Journal of the Korean Mathematical Society
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• v.59 no.6
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• pp.1153-1170
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• 2022

In this paper, we investigate the portfolio optimization problem under the SVCEV model, which is a hybrid model of constant elasticity of variance (CEV) and stochastic volatility, by taking into account of minimum-entropy robustness. The Hamilton-Jacobi-Bellman (HJB) equation is derived and the first two orders of optimal strategies are obtained by utilizing an asymptotic approximation approach. We also derive the first two orders of practical optimal strategies by knowing that the underlying Ornstein-Uhlenbeck process is not observable. Finally, we conduct numerical experiments and sensitivity analysis on the leading optimal strategy and the first correction term with respect to various values of the model parameters.

• East Asian Economic Review
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• v.25 no.1
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• pp.73-97
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• 2021

China has experienced many structural changes in the process of economic development over the past three decades. Using a time-varying parameter VAR model with stochastic volatility and mixture innovations, this study investigates whether such structural changes in, especially tools and operational aims of monetary policy, affect the monetary transmission mechanism. We find that impulse responses of output growth and inflation to monetary shocks have substantially increased and then reversed to decrease around 2005-2006. This time variation is mainly caused by changes in the monetary transmission mechanism, i.e., the manner in which main macroeconomic variables respond to policy shocks, rather than by changes in volatilities of exogenous shocks. The result implies that aggressive monetary policy to facilitate economic growth in the developing economies may be legitimized, unless it causes inflation seriously.

• KDI Journal of Economic Policy
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• v.44 no.4
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• pp.79-108
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• 2022

This study examines the impact of sentiment shock, which is defined as a stochastic innovation to the Housing Market Confidence Index (HMCI) that is orthogonal to past housing price changes, on aggregate housing price changes and housing price volatility. This paper documents empirical evidence that sentiment shock has a statistically significant relationship with Korea's aggregate housing price changes. Specifically, the key findings show that an increase in sentiment shock predicts a rise in the aggregate housing price and a drop in its volatility at the national level. For the Seoul Metropolitan Region (SMR), this study also suggests that sentiment shock is positively associated with one-month-ahead aggregate housing price changes, whereas an increase in sentiment volatility tends to increase housing price volatility as well. In addition, the out-of-sample forecasting exercises conducted here reveal that the prediction model endowed with sentiment shock and sentiment volatility outperforms other competing prediction models.

• Journal of the Korean Mathematical Society
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• v.43 no.4
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• pp.845-858
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• 2006

We present two approaches of the stochastic interest rate European option pricing model. One is a bond numeraire approach which is applicable to a nonzero value asset. In this approach, we assume log-normality of returns of the asset normalized by a bond whose maturity is the same as the expiration date of an option instead that of an asset itself. Another one is the expectation hypothesis approach for value zero asset which has futures-style margining. Bond numeraire approach allows us to calculate volatilities implied in options even though stochastic interest rate is considered.

• ETRI Journal
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• v.35 no.5
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• pp.849-858
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• 2013

In this paper, we propose a new adaptive single model to track a maneuvering target with abrupt accelerations. We utilize the stochastic differential equation to model acceleration of a maneuvering target with stochastic volatility (SV). We assume the generalized autoregressive conditional heteroscedasticity (GARCH) process as the model for the tracking procedure of the SV. In the proposed scheme, to track a high maneuvering target, we modify the Kalman filtering by introducing a new GARCH model for estimating SV. The proposed tracking algorithm operates in both the non-maneuvering and maneuvering modes, and, unlike the traditional decision-based model, the maneuver detection procedure is eliminated. Furthermore, we stress that the improved performance using the GARCH acceleration model is due to properties inherent in GARCH modeling itself that comply with maneuvering target trajectory. Moreover, the computational complexity of this model is more efficient than that of traditional methods. Finally, the effectiveness and capabilities of our proposed strategy are demonstrated and validated through Monte Carlo simulation studies.

• The Korean Journal of Financial Management
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• v.22 no.2
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• pp.43-69
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• 2005

This study provides empirical evidence that the stochastic beta model based on Bayesian analysis outperforms the existing conditional beta model and GARCH model in terms of the estimation accuracy and the explanatory power in the cross-section of stock returns in Korea. Betas estimated by the stochastic beta model explain $30{\sim}50%$ of the cross-sectional variation in stock-returns, whereas other time-varying beta models account for less than 3%. Such a difference in explanatory power across models turns out to come from the fact that the stochastic beta model absorbs the variation due to the market anomalies such as size, BE/ME, and idiosyncratic volatility. These results support the rational asset pricing model in that market anomalies are closely related to the variation of expected returns generated by time-varying betas.

• East Asian mathematical journal
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• v.40 no.1
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• pp.63-74
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• 2024

Timer options are financial instruments proposed by Société Générale Corporate and Investment Banking in 2007. Unlike vanilla options, where the expiry date is fixed, the expiry date of timer options is determined by the investor's choice, which is in linked to a variance budget. In this study, we derive a pricing formula for hybrid options that combine timer options, digital options, and power options, considering an environment where volatility of an underlying asset follows a fast-mean-reverting process. Additionally, we aim to validate the pricing accuracy of these analytical formulas by comparing them with the results obtained from Monte Carlo simulations. Finally, we conduct numerical studies on these options to analyze the impact of stochastic volatility on option's price with respect to various model parameters.

• Environmental and Resource Economics Review
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• v.31 no.3
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• pp.393-417
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• 2022

Using hourly SMP data from 2016 to 2020, this paper measures the weekly realized volatility and investigates the main force of its determinants. To this end, we extend the Bayesian variable selection by incorporating the regime-switching model which identifies important variables among a large number of predictors by regimes. We find that the increase in coal and nuclear generation, as well as solar power, reinforce the SMP volatility in both high volatility and low volatility regime. In contrast the increase in gas generation and gas price decrease SMP volatility when SMP volatility is high. These results suggest that the expansion of renewable energy according to 2050 Carbon Neutrality or energy transition policies increases SMP volatility but the increase in the gas generation or reduction of coal generation might offset its impact.