Time Variation in the Tail Behaviour of Bunds Futures Returns

36 Pages Posted: 7 Apr 2003

See all articles by Thomas Werner

Thomas Werner

European Central Bank (ECB)

Christian Upper

Bank for International Settlements (BIS)

Date Written: December 2002


The present paper focuses on three questions: (i) Are heavy tails a relevant feature of the distribution of BUND futures returns? (ii) Is the tail behaviour constant over time? (iii) If it is not, can we use the tail index as an indicator for financial market risk and does it add value in addition to classical indicators? The answers to these questions are (i) yes, (ii) no, and (iii) yes. The tail index is on average around 3, implying the nonexistence of the fourth moments. A recently developed test for changes in the tail behaviour indicated several breaks in the degree of heaviness of the return tails. Interestingly, the tails of the return distribution do not move in parallel to realised volatility. This suggests that the tails of futures returns contain information for risk management that complements those gained from more standard statistical measures.

Keywords: Tail index, futures returns, extreme value theory, risk management

JEL Classification: C14, G13

Suggested Citation

Werner, Thomas and Upper, Christian, Time Variation in the Tail Behaviour of Bunds Futures Returns (December 2002). Available at SSRN: https://ssrn.com/abstract=362320 or http://dx.doi.org/10.2139/ssrn.362320

Thomas Werner (Contact Author)

European Central Bank (ECB) ( email )

Sonnemannstrasse 22
Frankfurt am Main, 60314

Christian Upper

Bank for International Settlements (BIS) ( email )

Centralbahnplatz 2
Basel, Basel-Stadt 4002

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