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Annals of Civil Engineering and Management(ACEM)

ISSN: 3065-9779 | DOI: 10.33140/ACEM

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Review Article - (2026) Volume 3, Issue 2

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Urban Congestion as a Volatility Pricing Problem: A Call–Put Options Framework with Black–Scholes Travel Time Valuation

Paul T E Cusack *
 
BScE (Civil), Canada
 
*Corresponding Author: Paul T E Cusack, BScE (Civil), Canada

Received Date: May 13, 2026 / Accepted Date: Jun 08, 2026 / Published Date: Jun 16, 2026

Copyright: ©2026 Paul T E Cusack. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

Citation: Cusack, P. T. E. (2026). Urban Congestion as a Volatility Pricing Problem: A Call–Put Options Framework with Black–Scholes Travel Time Valuation. Ann Civ Eng Manag, 3(2), 01-03.

Abstract

This paper develops a unified financial-economics framework for urban congestion in which travel time is treated as a stochastic asset with density-dependent volatility. Automobile travel is modeled as a call option on low-congestion travel time, while transit and avoidance behavior act as put-like hedges against congestion risk. We embed a Black–Scholes- type valuation framework to price travel-time uncertainty and derive a congestion pricing rule equivalent to an option premium. Marginal external costs are shown to scale convexly with congestion-induced volatility, providing a structural basis for congestion pricing in urban systems.

Introduction

Urban congestion is traditionally modeled using marginal cost pricing:

MB = MC + MEC

However, this formulation omits a key empirical feature: travel time is stochastic and volatility increases with density. This paper reframes congestion as a financial options market over uncertain travel-time outcomes, where congestion externalities arise from unpriced volatility risk.

Travel Time as a Stochastic Process

Utility Function

U = V - c - αT

Call Option Interpretation (Automobile Travel)

Put Option Interpretation (Transit / Avoidance)

Transit acts as downside protection:

Marginal External Cost (Volatility Externality)

Black-Scholes Framework for Travel Time Valuation

Define the “Travel Asset”

Let:

• S = realized travel efficiency (inverse travel time)

• K = free-flow benchmark efficiency

• σ = congestion volatility

• t = travel horizon

• r = social discount rate

Black–Scholes Call Option (Driving Value)

Interpretation in Transportation Terms

Variable

Meaning

S

realized travel speed

K

free-flow speed

σ

congestion uncertainty

C

value of driving option

                                                                                                         Table1

Key Insight

Congestion Pricing from Black-Scholes Sensitivity

CMA Empirical Structure

Structural Results

Conclusion

This paper shows that urban congestion can be modeled as a Black–Scholes-style options market over stochastic travel time. Automobile travel behaves as a call option on free-flow mobility, while congestion externalities correspond to unpriced volatility exposure. Optimal congestion pricing is equivalent to an option premium that internalizes travel-time risk.

Final Core Result

Urban congestion is a Black–Scholes-style mispriced volatility market in which travel behaves as a call option on stochastic mobility, and marginal external costs arise from unpriced sensitivity to travel-time variance.

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