No arbitrage and lead–lag relationships

Hayashi, Teru; Koike, Yuta

doi:10.1016/j.spl.2019.06.006

Cited by 3 publications

(4 citation statements)

References 53 publications

(100 reference statements)

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“…hence we have P w m ρ J−j+1 (lτ J ), η > ε ε −1 (η + τ J )m by the Markov and Schwarz inequalities as well as (25). This yields (24).…”

Section: Proof Of Theoremmentioning

confidence: 75%

“…Next, (25) and the Schwarz inequality imply that E sup 0≤t≤m ρ J−j+1 (lτ Finally, for 0 ≤ s ≤ t ≤ m, the Schwarz inequality yields…”

Section: Proof Of Theoremmentioning

confidence: 95%

“…However, this is not the case if we take account of some market friction such as the discreteness of transaction times or transaction costs. In fact, in [25] it has been shown that the market with a constant risk-free asset and two risky assets whose log-price processes are respectively given by B 1 and B 2 defined in the above is free of arbitrage if we impose a minimal waiting time on subsequent transactions or take proportional transaction costs into consideration (see Section 3.2 of [25]).…”

Section: Model Specification Via Cross-spectrummentioning

confidence: 99%

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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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“…hence we have P w m ρ J−j+1 (lτ J ), η > ε ε −1 (η + τ J )m by the Markov and Schwarz inequalities as well as (25). This yields (24).…”

Section: Proof Of Theoremmentioning

confidence: 75%

“…Next, (25) and the Schwarz inequality imply that E sup 0≤t≤m ρ J−j+1 (lτ Finally, for 0 ≤ s ≤ t ≤ m, the Schwarz inequality yields…”

Section: Proof Of Theoremmentioning

confidence: 95%

Section: Model Specification Via Cross-spectrummentioning

confidence: 99%

See 1 more Smart Citation

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

Hayashi¹,

Koike

2018

SIAM J. Finan. Math.

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“…[9]). However, if we take account of market frictions such as discrete trading or transaction costs, we can show that our model has no arbitrage; see [17] for details.…”

Section: Settingmentioning

confidence: 88%

Multi-scale analysis of lead-lag relationships in high-frequency financial markets

Hayashi,

Koike

2017

Preprint

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We propose a novel estimation procedure for scale-by-scale lead-lag relationships of financial assets observed at high-frequency in a non-synchronous manner. The proposed estimation procedure does not require any interpolation processing of original datasets and is applicable to those with highest time resolution available. Consistency of the proposed estimators is shown under the continuous-time framework that has been developed in our previous work [16]. An empirical application shows promising results of the proposed approach.

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