Tail Wags Dog: Intraday Price Discovery in VIX Markets

Bollen, Nicolas P. B.; O’Neill, Michael; Whaley, Robert E.

doi:10.1002/fut.21805

Cited by 49 publications

(58 citation statements)

References 36 publications

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“…A similar model is studied in Robert & Rosenbaum [39] with a different methodology. Empirical applications of Hoffmann et al [27]'s methodology are found in [2,6,8,28]. Apart from Brownian motion driven models, the Hawkes processes may be a credible candidate to describe lead-lag effects in the continuous-time framework; see Bacry et al [3] and Da Fonseca & Zaatour [10] for example.…”

Section: Introductionmentioning

confidence: 99%

Wavelet-Based Methods for High-Frequency Lead-Lag Analysis

Hayashi¹,

Koike

2018

SIAM J. Finan. Math.

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We propose a novel framework to investigate lead-lag relationships between two financial assets. Our framework bridges a gap between continuous-time modeling based on Brownian motion and the existing wavelet methods for lead-lag analysis based on discrete-time models and enables us to analyze the multi-scale structure of lead-lag effects. We also present a statistical methodology for the scale-by-scale analysis of lead-lag effects in the proposed framework and develop an asymptotic theory applicable to a situation including stochastic volatilities and irregular sampling. Finally, we report several numerical experiments to demonstrate how our framework works in practice. J for some universal constant c 4 > 0, hence we obtainWe rewrite the target quantity as, we obtain (35) by the dominated convergence theorem once we prove Ξ J (i 1 , i 2 ) → 0 for any fixed i 1 , i 2 . By Lemma 7 we haveWe can take sufficiently large r such that 2/r < 1 − κ. Then we haveJ )|X]| r ] = O τ 1−2/r J L 2 log 2 τ J r/2 = o(1) by Lemma 12. This yields the desired result. N τ J by the triangle and Schwarz inequalities. Therefore, the Markov inequality yields P max l∈L + J |I J (l)| > ε ≤ ε −1 l∈L + J I J (l) 2 2 N 2 τ J for any ε > 0, hence max l∈L + J |I J (l)| → p 0.Noting that L 2 τ J → 0, we can prove max l∈L + J |II J (l)| → p 0 in an analogous manner to the above.Next we prove max l∈L + J |III J (l)| → p 0. For any k ∈ I m,N (i) we haveWe can prove max l∈L + J |IV J (l)| → p 0 in an analogous manner.Now we prove max l∈L + J |V J (l)| → p 0. By Lemma 14 and the boundedness of σ 1 and σ 2 , we haveψ 1 → 0 by assumptions. This especially implies that max l∈L + J |V J (l)| → p 0. Finally, by Lemmas 4(b) and 8 we have max l∈L + J |VI J (l)| = o p (M J · τ −1 J τ m · τ J ). Since M J = O(τ −1 m ), we obtain max l∈L + J |VI J (l)| → p 0. This completes the proof. Completion of the proof of Theorem 2We need the following auxiliary result:Lemma 15. Λ −j D(λ)Π(λ)e

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Section: Introductionmentioning

confidence: 99%

Wavelet-Based Methods for High-Frequency Lead-Lag Analysis

Hayashi¹,

Koike

2018

SIAM J. Finan. Math.

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“…Overall, Frijns et al (2016) conclude that the VIX futures have been increasingly more important to the price discovery process. Likewise, Bollen et al (2017) suggest that the VIX futures lagged the VIX in the first few years after its introduction, and show a increasing dominance of VIX futures over time. However, Bollen et al (2017) remark it remains an subtle and open question for the lead-lag relationships between the VIX and VIX futures.…”

Section: Introductionmentioning

confidence: 92%

“…Likewise, Bollen et al (2017) suggest that the VIX futures lagged the VIX in the first few years after its introduction, and show a increasing dominance of VIX futures over time. However, Bollen et al (2017) remark it remains an subtle and open question for the lead-lag relationships between the VIX and VIX futures. Additionally, Chen and Tsai (2017) reveal that the VIX futures play a dominant role in intraday price discovery.…”

Section: Introductionmentioning

confidence: 92%

Time-dependent lead-lag relationships between the VIX and VIX futures markets

Yang

Shao

2020

The North American Journal of Economics and Finance

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We utilize the symmetric thermal optimal path (TOPS) method to examine the dynamic interaction patterns between the VIX and VIX futures markets. We document that the VIX dominates the VIX futures more in the first few years, especially before the introduction of VIX options. We further observe that the TOPS paths show an alternate lead-lag relationship instead of a dominance between the VIX and VIX futures in most of the time periods. Meanwhile, we find that the VIX futures have been increasingly more important in the price discovery since the launch of several VIX ETPs.

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“…As a result, informed traders with large orders tend to divide their orders into several smaller trades and thus increase the number of transactions. In addition, Tsai, Chiu, and Wang (2015) investigate the informational role of quote changes in VIX options, and Bollen, O'Neill, and Whaley (2017) examine the price relation between the VIX index and its corresponding derivatives and find that VIX futures prices lead the VIX index. 7 For example, Shu and Zhang (2012) focus on the relation between daily VIX futures prices and the VIX index, and Frijns, Tourani-Rad, and Webb (2016), who conduct bi-directional Granger causality tests between these two markets, show that the effect appears to be stronger from VIX futures prices to the VIX.…”

mentioning

confidence: 99%

“…7 For example, Shu and Zhang (2012) focus on the relation between daily VIX futures prices and the VIX index, and Frijns, Tourani-Rad, and Webb (2016), who conduct bi-directional Granger causality tests between these two markets, show that the effect appears to be stronger from VIX futures prices to the VIX. In addition, Tsai, Chiu, and Wang (2015) investigate the informational role of quote changes in VIX options, and Bollen, O'Neill, and Whaley (2017) examine the price relation between the VIX index and its corresponding derivatives and find that VIX futures prices lead the VIX index. KAO ET AL.…”

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confidence: 99%

An analysis on the intraday trading activity of VIX derivatives

Kao¹,

Tsai

Wang

et al. 2017

Journal of Futures Markets

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We investigate the relation between trading activity in the VIX derivative markets and changes in the VIX index under a high‐frequency framework. We find a significant relation between the signed trading variables of VIX futures and the contemporaneous changes in the VIX index. In addition, the net signed trading variables of VIX futures are significant predictors of future changes in the VIX index. Our results provide support for the informational role of VIX futures and evidence that trading activity in VIX options is likely caused by temporary liquidity shocks rather than the likelihood of informed trading.

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Tail Wags Dog: Intraday Price Discovery in VIX Markets

Cited by 49 publications

References 36 publications

Wavelet-Based Methods for High-Frequency Lead-Lag Analysis

Wavelet-Based Methods for High-Frequency Lead-Lag Analysis

Time-dependent lead-lag relationships between the VIX and VIX futures markets

An analysis on the intraday trading activity of VIX derivatives

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