arXiv subjects

Chris Angstmann

Publications and source records attributed to Chris Angstmann.

5 recordsLinked to original sources

arXiv2026

Reaction-boundary variance and adjoint-consistent local-volatility projection

We derive an operational-time variance kernel for a latent-order-book reaction boundary and use it to separate three objects usually collapsed in calendar-time volatility models: a structural boundary cumulant, a clock projection, and a pricing-measure choice. The reaction boundary is the zero of a bid--ask imbalance field. For a locally linear book, signed order-flow perturbations displace this zero through a damped Abel response kernel, so the variance of boundary increments is obtained as a finite-scale Green-function cumulant rather than introduced as a primitive diffusion coefficient. For long-memory forcing with exponent $0<\gamma<1$, the operational variance has a closed asymptotic form involving effective signed-forcing intensity, liquidity slope, resilience, memory, and operational coarse-graining scale. A deterministic activity clock gives the benchmark local-volatility projection. More general, non-unique clocks generate candidate calendar-time pricing systems. We argue that such projections are admissible only when the induced forward density operator and backward valuation operator remain adjoint on the same state space. Adjoint consistency is therefore a reality constraint on operational-to-calendar time projection: it disciplines non-unique time and identifies where incompleteness enters.

q-fin.PR↗

arXiv2026

Revisiting Trade-sign Long-memory and Square-root Law price impact

Starting with a coupled discrete reaction--diffusion formulation for the lit and latent order books with non-uniformly sampled event times and meta-order source terms we show how two familiar market-microstructure regularities can emerge from this framework: the long-memory of trade signs associated with the Lillo--Mike--Farmer (LMF) theory and the square-root law (SQRL) of meta-order impact. This uses the locally linear order book and constant participation-rate execution in the front dynamics to reduce the dynamics to a Volterra equation whose leading-order solution then yields the well know result of concave impact trajectory, and a completion impact proportional to the square root of the meta-order size. We then use the interface representation to show how heavy-tailed Pareto meta-order lengths generate power-law trade-sign autocorrelations through the source term. These are familiar derivations, what is slightly different here is that we reinterpret these known derivations to make it clear that LMF law is an event-time sign-memory statement, whereas the square-root law is a physical-time viability statement where subordination can alter the calendar-time impact trajectories depending on the mappings and interpolation used to set continuum operational time.

q-fin.TR↗

arXiv2026

Correlation emergence and the Epps effect in two coupled limit order books

We give a unified analytic account of correlation emergence and the Epps effect in two coupled limit order books. The Epps effect is the empirical reduction in measured cross-asset log-return correlation at short aggregation scales, or equivalently the recovery of measured correlation as the aggregation interval increases. The model starts from a fixed-grid discrete random walk for order flow in operational time, with creation, cancellation and diffusion. A pair-trader coupling between the books is introduced at the level of order creation, and calendar time is imposed through separate observation clocks. We clarify how the operational-time model reduces to coupled reaction--diffusion equations with a moving reaction boundary defining the model log-mid-price. Using a regularised local-response representation of the coupling, we derive approximate closed-form expressions for realised correlations as a function of aggregation time. Here the Epps effect is shown to arise from two distinct mechanisms: asynchronous observation clocks (subordination), finite coupling response times, and their combination.

q-fin.TR↗

arXiv2026

Option prices from operational-time reaction-boundary lattices

We consider the role of a continuum operational time $u$, its mapping to calendar time $t$, and their relation to event time in option-pricing problems. We derive option-pricing equations from an operational-time Markov lattice rather than from a calendar-time diffusion. The primitive model is a homogeneous nearest-neighbour log-price lattice; state-dependent local variance is represented through its general local-kernel extension. Its Chapman--Kolmogorov decomposition yields discrete forward and backward equations. In price variables, the backward equation gives a generalized European pricing PDE and reduces to Black--Scholes--Merton under the risk-neutral drift restriction and constant volatility. Interpreted as a reaction boundary, the lattice gives a structural route from boundary variance to projected local volatility. The key point is the separation of the operational kernel, the calendar-time clock projection, and the pricing-measure choice. Within the deterministic one-factor local-volatility class, an option surface identifies the projected clock--variance combination rather than its operational variance and clock components separately. The resulting hierarchy also distinguishes full calendar-generator equivalence from weaker terminal or continuum matching, and clarifies why incompleteness concerns unspanned clock, jump, or renewal risks rather than random time alone.

q-fin.PR↗

arXiv2026

Non-unique time and market incompleteness

Financial markets are often modelled as if time were unique and continuous across assets and markets. Financial markets are however asynchronous, order flow is event-driven, and waiting times between events are often random. Many of the most influential formulations of financial market models presuppose a unique global calendar time and advocate for this or that preferred single latent continuous-time price system. Here we critically contrast these assumptions with event-time, renewal, point-process, and order-flow descriptions. We revisit no-arbitrage, no-dynamic-arbitrage, and risk-neutral option pricing in settings where the market is represented as a discrete event system and where the continuum limit of a discrete-time random walk need not be unique. The central suggestion is then that such non-uniqueness points to a more foundational form of market incompleteness than is usually emphasized. This highlights the importance of operational time at the level of decision making but reminds market practitioners that managing risk itself often requires reconciling operational time with a global calendar time. At these longer time scales forms of effective or average completeness may still emerge at lower frequencies and remain useful for portfolio construction and risk management, even if high-frequency hedging and execution expose a clock mismatch between trading, pricing, and longer-horizon allocation.

q-fin.TR↗