유위험 이자율 평가이론 검정을 위한 연속시간의 준모수적 모형

이은희 ( Eun Hee Lee ) 한국경제학회 2012 經濟學硏究 Vol.60 No.3

본 논문은 유위험이자율 평가이론(또는 커버되지 않는 이자율 평가이론)을 검정하기 위하여 연속시간의 준모수적 회귀모형을 고려하였다. 본 논문의 회귀모형은 두 국가간의 이자율의 차이로 유도되는 모수적 추세 함수와 위험프리미엄으로 정의되는 비모수 추세함수로 구성되는 두 개의 조건부 평균성분과 일반적인 마팅게 일차분과정으로 정의되는 오차항 성분으로 이루어져 있다. 위험프리미엄을 상수라고 가정할 경우 조건부 평균성분은 모두 모수적 형태로 일반적인 회귀모형을 따르게 된다. 반면 시가변적인 위험프리미엄을 가정할 경우, 위험프리미엄을 시간의 평활함수로 가정하고 시리즈 추정방법을 통해 추정하였다. 또한 일반적인 마팅게일차분과정을 따르는 오차성분에 존재하는 확률적 변동성을 효과적으로 교정하기 위해 시간변화라는 샘플링기법을 사용하였다. 따라서 적절한 표본 구간이 정해지면 유위험이자율 평가설은 도구변수추정방법을 통해 검증할 수 있다. 미국-영국과 미국-캐나다의 경우, 시가변적 위험프리미엄을 감안한 우리의 연속시간 유위험이자율평가 모형을 적용한 결과, 국내외금리차와 환율변화율의 음의 선형관계를 나타내는 유위험이자율 평가이론 퍼즐현상은 발견되지 않는다. 또한, 미국-한국의 사례에서 시가변적 위험프리미엄을 가정할 때, 보다 이론이 부합되는 회귀계수를 도출할 수 있었다. This paper considers a continuous-time semi-parametric regression model to test for the uncovered interest parity. The regression has two mean components, one parametric and the other nonparametric, with error term specified generally as a martingale differential. The parametric part in the mean is linear and derived under no arbitrage condition. To deal with the time-varying risk premium, we introduce an additional nonparametric term in the regression mean, which specifies the time-varying risk premium as general smooth function of time. To effectively deal with stochastic volatility in the general martingale differential regression error, we use a time change to set sampling intervals. Once the samples are collected at appropriate sample intervals, the uncovered interest parity condition is tested by a mixture of series and IV estimation methods. As a result from our work, for Canada and UK, the uncovered interest parity puzzle implying that interest rate differentials seem often to be followed by exchange rate depreciation is not supportive in our model. For Korea, we obtain more favorable coefficients for UIP condition.

On the Gerber-Shiu discounted penalty function in a risk model with delayed claims

Zou, Wei,Xie, Jie-Hua 한국통계학회 2012 Journal of the Korean Statistical Society Vol.41 No.3

In this paper, we consider an extension to the continuous time risk model for which the occurrence of the claim may be delayed and the time of delay for the claim is assumed to be random. Two types of dependent claims, main claims and by-claims, are defined, where every by-claim is induced by the main claim. The time of occurrence of a by-claim is later than that of its associate main claim and the time of delay for the occurrence of a by-claim is random. An integro-differential equations system for the Gerber-Shiu discounted penalty function is established using the auxiliary risk models. Both the system of Laplace transforms of the Gerber-Shiu discounted penalty functions and the Gerber-Shiu discounted penalty functions with zero initial surplus are obtained. From Lagrange interpolating theorem, we prove that the Gerber-Shiu discounted penalty function satisfies a defective renewal equation. Exact representation for the solution of this equation is derived through an associated compound geometric distribution. Finally, examples are given with claim sizes that have exponential and a mixture of exponential distributions.

On the Gerber–Shiu discounted penalty function in a risk model with delayed claims

Wei Zou,Jie-hua Xie 한국통계학회 2012 Journal of the Korean Statistical Society Vol.41 No.3

In this paper, we consider an extension to the continuous time risk model for which the occurrence of the claim may be delayed and the time of delay for the claim is assumed to be random. Two types of dependent claims, main claims and by-claims, are defined,where every by-claim is induced by the main claim. The time of occurrence of a by-claim is later than that of its associate main claim and the time of delay for the occurrence of a byclaim is random. An integro-differential equations system for the Gerber–Shiu discounted penalty function is established using the auxiliary risk models. Both the system of Laplace transforms of the Gerber–Shiu discounted penalty functions and the Gerber–Shiu discounted penalty functions with zero initial surplus are obtained. From Lagrange interpolating theorem, we prove that the Gerber–Shiu discounted penalty function satisfies a defective renewal equation. Exact representation for the solution of this equation is derived through an associated compound geometric distribution. Finally, examples are given with claim sizes that have exponential and a mixture of exponential distributions.

우리나라 주식수익률의 확률변동성 특성에 관한 연구

장국현 ( Kook Hyun Chang ) 한국재무관리학회 2003 財務管理硏究 Vol.20 No.1

This paper uses the Efficient Method of Moments(EMM) of Gallant and Tauchen to estimate continuous-time stochastic volatility diffusion model for the Korean Composite Stock Price Index, sampled daily over 1995∼2002. The estimates display non-normality of stock index return, leptokurtic distribution, and stochastic volatility. Further, this study suggests that two factor stochastic volatility model will be more desirable than one factor stochastic volatility model to estimate daily Korean stock return and also suggests that the stochastic volatility diffusions should allow for Poisson jumps of time-varying intensity.

ON THE PROBABILITY OF RUIN IN A CONTINUOUS RISK MODEL WITH DELAYED CLAIMS

Zou, Wei,Xie, Jie-Hua Korean Mathematical Society 2013 대한수학회지 Vol.50 No.1

In this paper, we consider a continuous time risk model involving two types of dependent claims, namely main claims and by-claims. The by-claim is induced by the main claim and the occurrence of by-claim may be delayed depending on associated main claim amount. Using Rouch$\acute{e}$'s theorem, we first derive the closed-form solution for the Laplace transform of the survival probability in the dependent risk model from an integro-differential equations system. Then, using the Laplace transform, we derive a defective renewal equation satisfied by the survival probability. For the exponential claim sizes, we present the explicit formula for the survival probability. We also illustrate the influence of the model parameters in the dependent risk model on the survival probability by numerical examples.

On the probability of ruin in a continuous risk model with delayed claims

Wei Zou,Jie-hua Xie 대한수학회 2013 대한수학회지 Vol.50 No.1

In this paper, we consider a continuous time risk model involving two types of dependent claims, namely main claims and by-claims. The by-claim is induced by the main claim and the occurrence of by-claim may be delayed depending on associated main claim amount. Using Rouche's theorem, we first derive the closed-form solution for the Laplace transform of the survival probability in the dependent risk model from an integro-differential equations system. Then, using the Laplace transform, we derive a defective renewal equation satisfied by the survival probability. For the exponential claim sizes, we present the explicit formula for the survival probability. We also illustrate the influence of the model parameters in the dependent risk model on the survival probability by numerical examples.

연속시간에서의 모호성 회피성향을 감안한 환위험프리미엄과 마팅게일 희귀분석

이은희(Eunhee Lee) 한국자료분석학회 2021 Journal of the Korean Data Analysis Society Vol.23 No.3

본 연구는 환율의 초과수익률을 모형화하기 위하여 모호성(ambiguity) 회피성향을 반영하는 다중 사전분포 재귀적 효용함수(multiple-priors recursive utility)를 기반으로 한 연속시간의 자산가격 결정모형을 제시하였다. 본 연구에서 제시하는 모형에 따르면, 환율의 초과수익률 확률과정의 조건부 평균부분은 환율과 소비성장률과의 공분산에 의해 설명되어지는 부분과 환율과 시장수익률과의 공분산으로 정의되는 부분 그리고 마지막으로 다중 사전분포에 대한 가정을 할 경우 추가적으로 반영되는 불확실성 프리미엄 부분으로 구성되어진다. 도출된 모형으로 부터 효용함수의 주요 모수를 추정하기 위해 마팅게일 회귀분석방법(martingale regression estimation)을 이용하였다. 모형에 대한 추정 결과를 요약하면, 멱 효용함수를 가정할 경우 상대위험회피도는 약 16으로 추정되었으며, 재귀적 효용함수를 가정할 경우 위험회피도는 약 14로 추정되었다. 반면, 모호성에 대한 회피성향을 반영한 재귀적 다중 사전분포 효용함수 모형의 경우, 상대위험회피도는 4로, 시점간 자원배분에 대한 대체탄력성의 경우 1보다 작지만 1에 근접한 값으로 통계적으로 유의하게 추정되었으며, 모호성회피성향은 약 0.08로 유의하게 추정되었다. 이와 같은 결과로부터, 외환시장의 환위험프리미엄을 설명하는 요인으로 불확실성의 고려가 중요함을 예측할 수 있다. This paper proposed the continuous time asset pricing model based on the multiple-priors recursive utility with ambiguity aversion in order to model exchange risk premium. According to the model, the conditional mean part in the excess exchange rate returns consists of the covariance between returns and consumption growths, the covariance between returns and financial wealth growths and the uncertainty premium. To estimate the parameters in the proposed model, I used the martingale regression estimation method. According to the estimation results for the parameters in preference using martingale regression estimation, the relative risk aversion(RRA) is significantly estimated around 4, and the elasticity of intertemporal substitution(EIS) is significantly estimated around 0.95. In addition, the ambiguity aversion parameter is also significantly estimated around 0.08. These results imply that uncertainty plays an important role in explaining the exchange rate premium in the currency market.

Ruin Probabilities in a Risk Model with Two Types of Claims

Han, Ji-Yeon,Choi, Seung-Kyoung,Lee, Eui-Yong The Korean Statistical Society 2012 응용통계연구 Vol.25 No.5

A surplus process with two types of claims is considered, where Type I claims occur more frequently, however, their sizes are smaller stochastically than Type II claims. The ruin probabilities of the surplus caused by each type of claim are obtained by establishing integro-differential equations for the ruin probabilities. The formulas of the ruin probabilities contain an infinite sum and convolutions that make the formulas hard to be applicable in practice; subsequently, we obtain explicit formulas for the ruin probabilities when the sizes of both types of claims are exponentially distributed. Finally, we show through a numerical example, that Type II claims have more impact on the ruin probability of the surplus than Type I claims.