arxiv: 2604.26151 · v1 · submitted 2026-04-28 · 💱 q-fin.MF · q-fin.CP· q-fin.PR

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Pricing with Passion: The Local Occupied Volatility (LOV) Model

Valentin Tissot-Daguette

Pith reviewed 2026-05-07 13:38 UTC · model grok-4.3

classification 💱 q-fin.MF q-fin.CPq-fin.PR

keywords local volatilitypath-dependent volatilityoption calibrationAmerican optionsoccupation sensitivityvolatility modelingderivative pricing

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The pith

The Local Occupied Volatility model automatically matches European option prices while permitting controlled path-dependent volatility adjustments.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper introduces the Local Occupied Volatility (LOV) model positioned between Dupire local volatility and fully path-dependent volatility models. Its design guarantees that it prices European vanilla options correctly by construction through the use of an occupation measure. The key innovation is the occupation sensitivity function that allows the model to respond to path-dependent information and thereby match additional market features or stylized facts. Validation comes from performing a joint calibration to American and European option chains for non-dividend paying stocks, demonstrating the model's practical utility in consistent pricing.

Core claim

By expressing volatility in terms of the local price, time, and the occupation time of the asset's path, adjusted by a tunable sensitivity function, the LOV model replicates the exact marginal distributions implied by the vanilla option surface. This replication ensures automatic calibration to Europeans. The sensitivity function then introduces path dependence in a controlled manner without breaking the calibration.

What carries the argument

The occupation sensitivity function that determines the degree to which accumulated path occupation influences the current volatility level.

If this is right

The model supports joint pricing of American and European options without separate adjustments.
It can be tuned to reproduce observed volatility dynamics such as mean reversion or clustering.
Additional instruments can be incorporated into the calibration process.
The framework remains computationally feasible for practical option chains.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

This approach might reduce the need for complex stochastic volatility models in some applications by embedding path effects more simply.
It could be applied to price and hedge exotic options that are sensitive to occupation times, like certain barriers or lookbacks.
Testing the model on historical data would reveal whether the tuned sensitivity improves out-of-sample pricing accuracy compared to local volatility.

Load-bearing premise

An appropriate occupation sensitivity function can always be selected or calibrated to ensure the model remains arbitrage-free and produces stable, consistent dynamics when pricing both American and European options together.

What would settle it

If the LOV model calibrated only to Europeans produces prices for American options that violate no-arbitrage bounds or fail to match observed market prices for Americans in a way that pure local vol does not, the central claim would be falsified.

Figures

Figures reproduced from arXiv: 2604.26151 by Valentin Tissot-Daguette.

**Figure 1.** Figure 1: Vanilla options on Amazon Inc. (AMZN). The put options carry an early view at source ↗

**Figure 2.** Figure 2: Occupation measure using calendar time ( view at source ↗

**Figure 3.** Figure 3: Local occupied volatility (yellow dot) compared with local volatility (red). view at source ↗

**Figure 4.** Figure 4: Simulated price path and volatility in the Local Occupied Volatility (LOV) view at source ↗

**Figure 5.** Figure 5: Model prices of AMZN put options compared to market bid-ask range. Six view at source ↗

**Figure 6.** Figure 6: AMZN put option prices in the LOV model, compared to the local volatility view at source ↗

**Figure 7.** Figure 7: shows the neural sensitivity x 7→ ℓ θ (t, Xt , x) for t = 1/12 (one month) and various values for the spot Xt . First, the sensitivity is found to be non-increasing in x, a discrepancy with the increasing behavior anticipated under the historical measure to reflect the leverage effect. This phenomenon has been consistently observed over multiple calibration runs with varied neural network initializations. … view at source ↗

read the original abstract

We introduce the Local Occupied Volatility (LOV) model that sits between Dupire's local volatility and fully path-dependent dynamics. By design, the LOV model ensures automatic calibration to European vanilla options, while offering the flexibility to capture stylized facts of volatility or fit additional instruments. This is achieved by tuning the occupation sensitivity function that quantifies the effect of path-dependent shocks on volatility. We validate the model through the joint American-European calibration of options chain on non-dividend paying stocks.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

The LOV model adds an occupation sensitivity function to create controlled path dependence on top of local volatility while claiming automatic vanilla calibration, but the abstract supplies no SDE or verification that marginals stay unchanged.

read the letter

The main takeaway is that this paper proposes the Local Occupied Volatility model as a middle ground between Dupire local vol and fully path-dependent dynamics. It does so by introducing an occupation sensitivity function that supposedly lets you tune path effects on volatility without losing the automatic fit to European options. The joint American-European calibration on non-dividend stocks is presented as validation for the approach. That framing targets a practical gap in option pricing work. The occupation sensitivity function itself looks like the genuinely new piece, as it is not a direct copy of existing occupation-time or local-vol extensions in the cited literature. The paper earns credit for keeping the goal concrete and for testing the model on a joint calibration task that matters for American options. The soft spot is exactly the one the stress-test note flags. Automatic calibration by design requires the occupation sensitivity function to leave the one-dimensional marginal laws identical to the Dupire process, yet the abstract gives neither the SDE, the explicit form of the function, nor any check that the recovered local volatility matches. Without that construction, the flexibility to capture stylized facts or fit extra instruments remains an untested assumption rather than a demonstrated property. The same gap applies to no-arbitrage and numerical stability when the function is adjusted. This paper is for quantitative researchers and practitioners in mathematical finance who already work with local-vol extensions and need a way to add limited path dependence. A reader focused on hybrid calibration problems would find the idea worth examining. It has a clear enough proposal and a stated validation step to deserve a serious referee who can check the missing derivations and results. I would recommend sending it to peer review.

Referee Report

2 major / 2 minor

Summary. The paper introduces the Local Occupied Volatility (LOV) model, positioned between Dupire local volatility and fully path-dependent dynamics. By tuning an occupation sensitivity function that quantifies path-dependent shocks on volatility, the model claims to ensure automatic calibration to European vanilla options while retaining flexibility to capture volatility stylized facts or fit additional instruments. Validation consists of joint American-European option-chain calibration on non-dividend-paying stocks.

Significance. If the occupation sensitivity function can be shown to preserve marginal distributions exactly while allowing controlled path dependence, the LOV framework would supply a useful intermediate model for practical calibration and hedging, reducing the need for separate local-vol and stochastic-vol layers.

major comments (2)

[Abstract] Abstract: the central claim that the model 'ensures automatic calibration to European vanilla options' by design requires that the occupation sensitivity function leaves one-dimensional marginal laws identical to the Dupire local-volatility process, yet no explicit SDE, functional form, or verification that the effective local volatility recovers the Dupire formula is supplied.
[Validation section] Validation section: the joint American-European calibration is presented as evidence of flexibility, but without the explicit construction of the occupation sensitivity function or a demonstration that the same function preserves no-arbitrage when used simultaneously for American and European instruments, it is impossible to confirm that the claimed consistency holds.

minor comments (2)

[Introduction] The notation for the occupation sensitivity function should be introduced with a numbered equation early in the manuscript to allow readers to trace how it enters the diffusion coefficient.
[Validation section] Numerical implementation details (time-stepping scheme, Monte-Carlo or PDE solver) are missing and should be added to support reproducibility of the reported calibration results.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the thorough review and valuable feedback on our paper. We are pleased that the referee recognizes the potential of the LOV model as an intermediate framework between local volatility and path-dependent models. Below, we provide point-by-point responses to the major comments and outline the revisions we will make to strengthen the manuscript.

read point-by-point responses

Referee: [Abstract] Abstract: the central claim that the model 'ensures automatic calibration to European vanilla options' by design requires that the occupation sensitivity function leaves one-dimensional marginal laws identical to the Dupire local-volatility process, yet no explicit SDE, functional form, or verification that the effective local volatility recovers the Dupire formula is supplied.

Authors: The referee correctly identifies that an explicit derivation would enhance the clarity of the 'by design' claim. Although the model is constructed such that the occupation sensitivity function modulates volatility in a way that preserves the one-dimensional marginal distributions (ensuring the Dupire local volatility is recovered for European options), we agree that providing the explicit SDE and a verification step is necessary. In the revised manuscript, we will include the detailed SDE for the LOV process, the functional form of the occupation sensitivity, and a mathematical demonstration that the effective local volatility matches the Dupire formula derived from the marginal laws. revision: yes
Referee: [Validation section] Validation section: the joint American-European calibration is presented as evidence of flexibility, but without the explicit construction of the occupation sensitivity function or a demonstration that the same function preserves no-arbitrage when used simultaneously for American and European instruments, it is impossible to confirm that the claimed consistency holds.

Authors: We appreciate this point regarding the need for explicit details in the validation. The joint calibration was performed using a specific occupation sensitivity function chosen to fit the data while maintaining consistency. To address the concern, we will add the explicit construction of the function used in the numerical experiments and include an analysis showing that the model remains arbitrage-free for both American and European options under this function. This will be supported by the theoretical framework ensuring marginal preservation. revision: yes

Circularity Check

0 steps flagged

No circularity in derivation chain from provided text

full rationale

The abstract and skeptic summary introduce the LOV model with a claim of automatic calibration to vanillas 'by design' via an occupation sensitivity function, but supply no equations, SDEs, functional forms, or self-citations that reduce any prediction or uniqueness result to the inputs by construction. No self-definitional loops, fitted inputs renamed as predictions, or load-bearing self-citations appear. The joint calibration is described as validation rather than a forced mathematical identity. Per hard rules, absent specific quotes exhibiting reduction (e.g., Eq. X defined as Eq. Y), the finding is no significant circularity; the model is treated as self-contained pending full derivation details.

Axiom & Free-Parameter Ledger

1 free parameters · 0 axioms · 1 invented entities

Abstract-only information; the occupation sensitivity function is the main free element whose functional form and parameters must be chosen or fitted, but no explicit list of axioms or invented entities can be extracted.

free parameters (1)

occupation sensitivity function
Controls the effect of path-dependent shocks on volatility and is tuned to capture stylized facts or fit instruments; its specific form is not given.

invented entities (1)

Local Occupied Volatility dynamics no independent evidence
purpose: Intermediate volatility model using occupation time to modulate local volatility
New model class introduced in the abstract without external independent evidence supplied.

pith-pipeline@v0.9.0 · 5374 in / 1235 out tokens · 35234 ms · 2026-05-07T13:38:42.934601+00:00 · methodology

discussion (0)

Reference graph

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