• Korean Journal of Mathematics
• /
• 제20권1호
• /
• pp.47-60
• /
• 2012

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

• 경제분석
• /
• 제25권3호
• /
• pp.70-99
• /
• 2019

본 연구는 주가지수, 원달러 환율, 국채수익률 및 신용스프레드로 구성된 Stochastic volatility-in-mean VAR 모형을 이용하여 금융시장 불확실성이 금융시장에 미치는 효과를 분석하였다. 첫째, 불확실성 증가충격의 효과는 경기후퇴적(recessionary)이며, 특히 주가 하락효과와 원달러 환율 상승효과가 강력한 것으로 나타났다. 둘째, 금융시장 스트레스에 따른 국면전환(regime shift) 효과에 대한 분석에서는 금융시장 위기 기간 중 불확실성의 효과가 평상시에 비해 더욱 강력해진다는 결과를 얻었다. 마지막으로 금융시장 불확실성 증가는 금융부문을 넘어 실물부문까지 영향을 미치는 실질효과 가능성에 대한 증거가 제시되었다.

• 대한수학회지
• /
• 제59권6호
• /
• pp.1153-1170
• /
• 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
• /
• 제25권1호
• /
• pp.73-97
• /
• 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
• /
• 제44권4호
• /
• pp.79-108
• /
• 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.

• 대한수학회지
• /
• 제43권4호
• /
• pp.845-858
• /
• 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
• /
• 제35권5호
• /
• pp.849-858
• /
• 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.

• 재무관리연구
• /
• 제22권2호
• /
• pp.43-69
• /
• 2005

본 논문은 한국 주식시장에서 CAPM 베타의 시간에 따른 변동패턴을 설명하는데 있어서 베이지안 분석기법에 기반을 둔 확률베타모형(stochastic be model)이 기존의 조건부 베타모형이나 이변량 GARCH(1,1)모형보다 추정의 정확도나 베타의 설명력 측면에서 더 우월하다는 실증적 증거를 보여주었다. 확률베타모형으로 추정한 베타는 주식수익률의 횡단면 변동의 $30{\sim}50%$를 설명하는 반면, 다른 시변베타모형은 3% 이하의 설명력에 그쳤다. 이렇게 확률베타모형에서 추정된 베타의 높은 설명력은 흔히 시장이상현상으로 받아들여지고 있는 기업규모효과나 장부가/시가비율효과, 고유변동성효과들을 대부분 흡수하는 것으로 나타났다. 이것은 시장이상 현상들이 베타 참값의 변동과 밀접하게 관련되어 있으며, 기대수익률 변동과 깊은 관련이 있다는 합리적 자산가격결정의 입장을 지지하는 것으로 해석된다.

• East Asian mathematical journal
• /
• 제40권1호
• /
• pp.63-74
• /
• 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.

• 자원ㆍ환경경제연구
• /
• 제31권3호
• /
• pp.393-417
• /
• 2022

전력시장 도매가격인 전력계통한계가격(System Marginal Price, SMP)의 급등락은 발전 사업자들의 재생에너지 및 기존 신규 발전설비에 대한 투자 결정을 변경하거나 지연시켜 에너지 정책 실현에 부정적인 영향을 미칠 수 있다. 이 연구는 2016~2020년 시간별 데이터를 활용하여 우리나라 SMP 주간 실현 변동성을 측정하고 결정요인을 파악함으로써 SMP 급등락 현상에 대한 정보 제공을 목적으로 한다. 국면전환(regime-switching)을 베이지안 변수선택(Bayesian stochastic selection) 모형에 적용하여 추정한 결과, SMP 고변동·저변동 국면 모두에서 기저 발전인 석탄 및 원자력 발전과 재생에너지인 태양광 발전의 증가는 SMP 변동성을 심화시키고, 가스발전량과 LNG 가격 변화는 고변동 국면에서만 SMP 변동성을 감소시키는 것으로 나타났다. 이러한 결과는 탄소 중립이나 에너지 전환 정책에 따른 재생에너지의 점진적인 확대가 SMP 변동성을 확대할 수 있지만, 재생에너지의 간헐성을 보완하기 위한 가스발전의 증가나 탄소 중립을 위한 석탄발전 감축은 SMP 변동성 증가를 상쇄시키는 역할을 할 수 있음을 시사한다.