Van Vliet gives a desk three tests and runs none of them. His model rests on one restriction, which he calls its central distinguishing implication. Squaring the news mark imposes it. Estimation plays no part.
Trades arrive with intensity λt = μ(t) + ηX + γY. A deterministic bathtub supplies the first term: ν + a_L e^(-κ_L t) + a_R e^(-κ_R(T-t)). It gives the familiar heavy open, dead midday and heavy close. Past trade sizes drive the second term, with self-excitation fading at rate ω. Trades beget trades. News pressure supplies the third.
News follows a Poisson point process with finite rate ρ_M. Each event has a signed mark h = r·s·n, combining relevance, sentiment and novelty. The news state jumps by h², then decays at rate υ. The underlying idea is old and sound. Markets run on information time, making volume, realized variance and execution risk different views of the same arrival rate. Van Vliet writes that rate explicitly.
The price equation uses the same marks. At every news event, the log midpoint moves by χh + σ_ε ε, alongside trade-time impacts J_k. News sign therefore moves price, while squared news moves the clock. Van Vliet is right to call this cross-equation restriction the distinctive piece. Hawkes intensities with time-varying backgrounds and news kernels already exist, as the paper acknowledges through citations to Rambaldi and colleagues and Omi and colleagues.
No empirical evidence supports the restriction, by design. The paper describes itself as theoretical. Its Appendix proves a diffusive limit for the trade-time log price using Rebolledo's martingale FCLT. The resulting variance is σ² = m_J² λ̄, where λ̄ = (μ̄ + γρ_M m₂/υ)/(1 - ηḡ/ω). The model requires subcriticality ηḡ/ω < 1. With independent news noise added, σ²_total = m_J² λ̄ + ρ_M σ_ε².
One simulated 390-minute session is the entire quantitative output. Event-driven thinning generates it after a 60-minute premarket burn-in, with an opening auction of size 400. The parameters are ν = 2, a_L = a_R = 30, κ_L = κ_R = 0.2, η = 0.15, ω = 0.3, γ = 120, υ = 0.5, ρ_M = 0.03 news per minute, χ = 0.0025. The author chose them to make all three components visible. They "are not calibrated to a particular asset or trading day".
Van Vliet directly defends showing a single session. "The objective is to demonstrate the interactions among the three components rather than to perform a statistical calibration." He also writes that "reporting a single simulated day is sufficient as opposed to estimating sampling properties over many days." Even on those terms, the defence gives a desk too little. Seeing three mechanisms on one path cannot establish whether prints allow γ, η and ω to be recovered separately.
The square creates the symmetry
The restriction is sharp, and the paper states it as a regression a desk could run tomorrow. Bucket news events, control for the baseline and trade-feedback state, then fit residual intensity on signed h and h². The predicted coefficient on signed h is zero. On h², the coefficient is γe^(-υu) ≥ 0.
The price equation predicts d₁ = χ > 0 on signed h and d₂ = 0 on h². Good and bad news of equal magnitude should produce identical activity and residual variance, with opposite price direction. For one event, cumulative residual variance is V_res(U;h) = σ_ε² + (m_J²γh²/υ)(1 - e^(-υU)). Construction alone makes it identical for +h and -h.
I would not bet on b_u = 0 surviving. At matched |h|, I expect a larger intensity response to negative marks.
His defence weakens the test
Van Vliet sees the issue. The paper says the model "deliberately imposes a symmetric activity response through h(x)²", conditional on assessed magnitude. Behavioural extensions, it suggests, could assign different γ loadings to gains and losses. The defence appears in the same passage: h "should be interpreted as the market's assessed news signal rather than as an untransformed objective announcement surprise". Framing and loss aversion can therefore enter through the mapping from the world into r, s and n.
Tractability comes at the test's expense. Once asymmetry can disappear into the assessed signal, rejection of b_u = 0 bears only on the scoring that produced r, s and n. It says nothing decisive about the model. The odd/even split earns its appeal from being checkable against transaction data. A mark free to absorb the residual removes that check.
Pick one.
If h is a score that can be constructed and timestamped, the symmetry prediction has content. I expect the downside response to exceed the upside response at matched |h|. If h remains latent, the third proposed test has no force as a test.
We reviewed a paper in which adding EGARCH asymmetry produced no forecasting edge over plain GARCH (our note), while the model ranking changed with the loss function. Daily return volatility therefore offers Van Vliet some support. Trade counts and volume immediately after a signed headline are a different object. Here, news pressure decays at υ = 0.5 per minute, meaning a jump loses half its size in roughly 1.4 minutes.
What the closed-form VWAP delivers
The VWAP result remains a derivation without a demonstration. Exponential kernels give u*(t) = Q·E(λt)/∫E(λs)ds in closed form. E(Y_t) also solves in one line, provided news arrives at constant rate ρ_M. Yet the paper motivates symmetric activity bursts with CPI and FOMC, whose release times everyone knows in advance.
The likelihood is safe because estimation conditions on the observed news path. The volume curve faces the problem. On practical value, the paper says an adaptive schedule based on realized X and Y "may reduce tracking error on high-news days" against a μ(t)-only baseline. The text reports no measured improvement over that baseline.
A fitter should know two further points before approaching the likelihood. The intensity sees (η, α) only through their product and (γ, β) only through theirs. The model consequently normalizes α = β = 1, leaving nine parameters. Van Vliet writes that "Mild regularization on γ may be used to reduce finite-sample overfitting", with γ the only parameter proposed for regularization.
He also says the parameterization remains low-dimensional and that baseline, feedback and news load on distinct variation, aiding identification. No estimation of any kind tests that assertion. In the simulation, the branching ratio ηḡ/ω is exactly 0.5. Under the standard interpretation of a branching ratio, half of order flow is endogenous. That share was chosen rather than measured.
We could not test any of these claims. The intensity is defined for individual trade arrivals carrying size marks, while the price equation uses the midpoint log price. Our data consist of one-minute bars. Without prints and quotes, there is no λ to estimate and no trade-time martingale against which to check m_J².
One table would change my mind: event-time intensity responses from real prints, estimated separately for positive and negative marks at matched |h|, with the two curves failing to separate. Van Vliet has specified exactly the model that would make such a table valuable. Until it exists, γ = 120 against a floor of ν = 2 remains a picture.