以極值理論研究基差尾端波動與其投資策略

The Study for Tail Behavior of Basis and the Investment Strategies under Extreme Value Theory

陳怡錫(Yi-Hsing Chen)

指導教授 ： 張國華

中原大學/工學院/工業工程研究所/碩士(2006年)

https://doi.org/10.6840/cycu200600404

摘要

本研究主要在利用個別探討基差左右尾端波動行為來分析其套利機會，而此
尾端波動行為之建立是結合考慮到期日效應之擴展後GARCH 模型與極值理論
中之Peak-over-Threshold (POT)方法。利用擴展後GARCH 模型估計每天之基差
變異數並將基差利用此變異數作轉換，再經由POT 方法將轉換後之基差配適為
極值理論中三種尾端型態之一。經過配適後，本研究發現基差右尾波動呈 Frechet
(厚尾) 型態而左尾波動呈Weibull(短尾)型態，其可能隱含意義為正基差的套利
機會較負基差存在更大的期望報酬。接著利用配適後之左右尾波動分配與擴展後
GARCH 模型模擬契約期間基差最大、最小值，進而估計出套利機會在給定信心
水準下進場的上下界臨界值，當正負基差超越估計的臨界值時，即進行在現貨與
期貨市場中一買一賣的操作，這裡的現貨是採用一線性規劃求解來決定追蹤標的
指數的市場投資組合，利用市場投資組合與期貨建立套利部位。此外，為了降低
到期日基差收斂不足的風險，本研究另提出一提前平倉策略，利用相同方法估計
出場之上下臨界值，經由實證證實若存在一足夠有利之出場條件下，提前平倉策
略較到期結算策略可獲得更高之報酬。

關鍵字

GARCH ； 極值理論 ； 到期日效應 ； 基差

並列摘要

In this thesis, the opportunity of basis arbitrage is discussed with the tail behavior
of daily basis for two sides respectively. The tail behavior of daily basis is
modeled by an augmented GARCH model with time-to-maturity variable and Peakover-
Threshold (POT) method suggested by extreme value theory (EVT). The augmented
GARCH model is to estimate the current volatility of the basis and Peakover-
Threshold method is to model the tail distributions of the standardized data
transformed by the estimated standard deviation from GARCH model. In the implementation,
the right tail distribution of basis is found to be Frechet (fat-tailed)
type and the left tail distribution is found to be Weibull (short-tailed) type, which
implies the arbitrage opportunity exist more expected profit in positive basis than
negative basis. Afterward, in order to grab a proper arbitrage opportunity, a bounded
criterion for two sides is built based on the estimation of maximum basis for whole
period of futures contracts which will be done by the fitted GARCH-GPD model and
a combined simulation method. Furthermore, in order to reduce the risk arising from
violation of zero basis at maturity date, another type of criterions is also set by the
GARCH-GPD model to determine the timing to close the positions before maturity
date and found that the corresponding outcomes generate a better performance than
those with the strategy which positions will be settled at maturity date. Interestingly,
both results from the strategies achieve the anticipative goal which is higher than the
deposit rate and independent of market.

並列關鍵字

Maturity effect ； GARCH ； Extreme value theory ； Basis

參考文獻

[13] Chiu, Y. C. and I.Y. Chuang, (2005) ” Performance Evaluation of Value at Risk

[14] Chien, M. H. (2004) ” An Alternative Approach of Taiwan Stock Index Futures

[12] Chi, C. J. (2004) ” A Study of ETFs in Arbitrage of Taiwan Stock Index Futures,”

[1] Anderson R. W. and J. P. Danthine (1983) ” The Time Pattern of Hedging and

[22] MacKinlay, A. C. and K. Ramaswamy, (1988) ” Index-Futures Arbitrage and the