Link Travel Time Estimation in Double-Queue-Based Traffic Models

Double queue concept has gained its popularity in dynamic user equilibrium (DUE) modeling because it can properly model real traffic dynamics. While directly solving such double-queue-based DUE problems is extremely challenging, an approximation scheme called first-order approximation was proposed to simplify the link travel time estimation of DUE problems in a recent study without evaluating its properties and performance. This paper focuses on directly investigating the First-In-First-Out property and the performance of the first-order approximation in link travel time estimation by designing and modeling dynamic network loading (DNL) on single-line stretch networks. After model formulation, we analyze the First-In-First-Out (FIFO) property of the first-order approximation. Then a series of numerical experiments is conducted to demonstrate the FIFO property of the first-order approximation, and to compare its performance with those using the second-order approximation, a point queue model, and the cumulative inflow and exit flow curves. The numerical results show that the first-order approximation does not guarantee FIFO and also suggest that the second-order approximation is recommended especially when the link exit flow is increasing. The study provides guidance for further study on proposing new methods to better estimate link travel times.

Approximation Formula for Option Prices under Rough Heston Model and Short-Time Implied Volatility Behavior

Rough Heston model possesses some stylized facts that can be used to describe the stock market, i.e., markets are highly endogenous, no statistical arbitrage mechanism, liquidity asymmetry for buy and sell order, and the presence of metaorders. This paper presents an efficient alternative to compute option prices under the rough Heston model. Through the decomposition formula of the option price under the rough Heston model, we manage to obtain an approximation formula for option prices that is simpler to compute and requires less computational effort than the Fourier inversion method. In addition, we establish finite error bounds of approximation formula of option prices under the rough Heston model for 0.1≤H<0.5 under a simple assumption. Then, the second part of the work focuses on the short-time implied volatility behavior where we use a second-order approximation on the implied volatility to match the terms of Taylor expansion of call option prices. One of the key results that we manage to obtain is that the second-order approximation for implied volatility (derived by matching coefficients of the Taylor expansion) possesses explosive behavior for the short-time term structure of at-the-money implied volatility skew, which is also present in the short-time option prices under rough Heston dynamics. Numerical experiments were conducted to verify the effectiveness of the approximation formula of option prices and the formulas for the short-time term structure of at-the-money implied volatility skew.