초고빈도 환율의 불연속 점프 변동성과 주기성에 대한 비모수적 추정 (Nonparametric Estimation of Discontinuous Jump Volatility and Periodicity in Ultra-High Frequency Foreign Exchange Rate)

서지정보

· 발행기관 : 한국금융학회
· 수록지 정보 : 금융연구 / 28권 / 1호 / 65 ~ 98페이지
· 저자명 : 이재득

초록

본 연구는 최근 2003년~2010년 동안의 한국 원화의 대 미국 달러 환율의 변동성을 분석하기위하여 극히 최근에 연구되기 시작한 비모수적 실현 변동성 파워이론을 도입하여, 5분간의초고빈도 자료들인 581,400개 관측치를 사용하여 원화 환율의 점프 변동성과 점프발생 확률에대한 비모수적 추정과 실증분석을 하였다. 본 연구결과 ROWV와 ROWQ 등을 도입하지만주기성의 변동성에 대한 주기성 필터를 사용하지 않았을 때는 2000년부터 2010년 9월 말까지한국 원화의 대 미국 달러 환율에 대해 점프가 발생할 확률이 아주 높게 나타났다. 반면에 최근에개발된 변동성의 여러 가지 주기성 필터인 MAD, Short Half Scale, 그리고 WSD 등을 사용하여점프 확률을 여러 가지로 점프 통계량으로 분석해본 결과, MAD의 주기성 필터를 사용하였을때는 주기성 필터를 사용하지 않을 때와 다소 비슷하게 나타났으나 다른 주기성 필터인 ShortHalf Scale 필터를 사용할 때는 약 66%의 점프가 발생할 확률을 보여 점프 발생확률이 상당히낮게 나타났고, WSD의 주기성 필터를 도입하였을 때는 약 49%의 점프가 발생할 확률이 나타나더욱 더 원화 환율의 점프 발생빈도가 낮게 나타났다. 일중 관측치를 사용하고 최고 이상치(maxoutlying)를 사용하여 점프 발생확률을 보면, 주기성 필터를 사용하지 않는 경우와 MAD 사용할때는 아주 작게 점프 발생빈도가 줄었지만, Short Half Scale를 사용할 때는 62.45%, 그리고 WSD등을 사용하였을 때는 47.21% 등으로 각각 점프 발생확률이 많이 줄어들었다. 일중내 기간관측치를 사용하였을 때는 역시 주기성 필터를 사용하지 않는 경우와 MAD 필터를 사용하는경우는 점프 발생빈도가 비슷하게 나타난 반면, Short Half Scale를 사용할 때는 65.44%, 그리고WSD 등을 사용하였을 때는 49.12% 등으로 점프 발생확률이 많이 줄어들었다.

영어초록

The parametric approaches such as the ARCH class of the models andstochastic volatility models, however, rely on explicit functional forms whichcan be misspecified and mainly low frequency financial data. Furthermore,the parametric approaches are very difficult to capture the properties ofmicrostructure of financial markets and announcement effects of importantfinancial and economic information. To overcome this drawback of theparametric approach, in recent years a few studies adopt nonparametricapproaches which are free from specific functional forms using ultra highfrequency financial data.
Thus this paper uses a new nonparametric realized volatility modelby summing intraday returns to analyze the discrete jumps as well ascontinuous volatility in returns of the exchange rate of Korean won. Firstof all, this paper introduces and analyzes the realized volatility, bipowervolatility, tripower quarticity, quadpower quarticity and relative jump modelsand then estimate whether the jumps are significant or not according toseveral derived jump statistics. Then this paper estimates whether the jumpsare significant or not according to derived jump statistics which are derivedfrom the realized volatility variables.
Then this paper compares the discrete jump volatility of the exchangerate returns of Korean won versus US dollar using the ultra-high frequencyfive minute returns spanning the period from year 2003 through 2010. Thispaper also includes the Realized Outlyingness Weighted Variance (ROWV)and Realized Outlying Weighted Quarticity (ROWQ) to obtain more efficientand robust jump estimates. Furthermore, this paper includes the periodicityfilters of volatility such as median absolute deviation (MAD), Short HalfScale estimator and Weighted Standard deviation (WSD) to analyze and toidentify whether the jumps are significant or not according to derived jumpstatistics. These estimators have the advantage that they are little affectedby jumps affecting two contiguous returns and periodicity.
The proposed robust estimation and jump detection depend on ROWVand ROWQ, and the several periodicity filters such as MAD, Short Half Scale,and WSD. Thus this paper compares the results of jumps detection usingnon filtered return tests and the filtered return tests with max outlyingness.This paper finds that if we include periodicity filters such as MAD, ShortHalf Scale and WSD, jumps occurred less frequently and the proportionof days with significant jumps of the exchange rate returns of Korean wonversus US dollar appeared smaller during years 2003 through 2010.
Firstly, when we did not use any periodicity filters, jump probabilitiesin the exchange rate returns of Korean won versus US dollar appeared higherthan 82% at the common critical levels. Secondly, we use Short Half Scalefilters, we have the approximate 66% of jump probabilities in the exchangerate returns of Korean won versus US dollar at the common critical levels.
Thirdly, when we use WSD filters, we have the approximate 49% ofjump probability so that five minute returns in the exchange rate returnsof Korean won versus US dollar have the discrete frequent jumps inapproximately two days during years 2003 through 2010.
Then we consider the max outlyingness as well as the periodicity filterssuch as MAD, Short Half Scale and WSD in jump statitics. First of all, weuse intraday observations. While when we do not consider any periodicityfilter, the jump probabilities of the realized returns of Korean won versusUS dollar appeared approximately 77%, when we do consider periodicityfilters such as MAD, Short Half Scale and WSD, the jump probabilities ofthe realized returns of Korean won appeared 77%, 62% and 47% at =0.999,respectively.
Then we use intraday periods. While when we do not consider anyperiodicity filter, the jump probabilities of the realized returns of Koreanwon versus US dollar appeared approximately 81%, when we do considerperiodicity filters such as MAD, Short Half Scale and WSD, the jumpprobabilities of the realized returns of Korean won appeared approximately80%, 65% and 48%, respectively.
Thus we found that when we consider periodicity filters such as MAD,Short Half Scale and WSD in jump statistics, jumps in the exchange ratereturns of Korean won versus US dollar occurred also less frequently andthe proportion of days with significant jumps in the exchange rate returnsof Korean won are also smaller.
Thus the jump probabilities for five minute returns of the exchangerate of Korean won versus US dollar spanning the period from year 2003through 2010 can be different according to which jump statistic we use.When we use the robust periodicity estimation such as MAD, Short HalfScale and WSD in jump probabilities, five minute returns in the exchangerate returns of Korean won versus US dollar have shown less frequent jumps.

참고자료

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