Small‐time, large‐time, and asymptotics for the Rough Heston model

2020 ◽  
Author(s):  
Martin Forde ◽  
Stefan Gerhold ◽  
Benjamin Smith
Keyword(s):  
Large Time ◽  
Small Time ◽  
Heston Model

Compact Algebraic Asymptotes for Small and Large Time Surface Temperatures for Regular Solid Bodies Heated With Uniform Heat Flux: Scrutiny of New Critical Fourier Numbers

2020 ◽  
Vol 13 (3) ◽  
Author(s):  
Agustín M. Delgado-Torres ◽  
Antonio Campo ◽  
Yunesky Masip-Macia
Keyword(s):  
Heat Flux ◽  
Large Time ◽  
Small Time ◽  
Uniform Heat Flux ◽  
Dimensionless Time ◽  
Time Approximation ◽  
Surface Temperatures ◽  
Uniform Heat ◽  
Relative Errors ◽  
Solid Bodies

Abstract The alternate infinite series at “small time” have been used to analyze the time variation of surface temperatures (ϕs) in regular solid bodies heated with uniform heat flux. In this way, compact algebraic asymptotes are successfully retrieved for ϕs in a plate, cylinder, and sphere in the “small time” sub-domain extending from 0 to the critical dimensionless time or critical Fourier number. For the “large time” sub-domain, the exact solution is approximated in two ways: with the “one-term” series and with the simple asymptotes corresponding to extreme “large time” conditions. Maximum relative errors of 1.23%, 6.24%, and 0.96% in ϕs for the plate, cylinder, and sphere are τcr obtained, respectively, with the “small time”—“large time” approximation using a traditional approach to fix the τcr value. An alternative approach to set the τcr is proposed to minimize the maximum relative error of the approximated solutions so that values of 1.19%, 3.93%, and 0.16% are then obtained for the plate, cylinder, and sphere, respectively, with the “small time”—“large time” approximation. For the “small time”—“one-term” approximation maximum relative errors of 0.024%, 1.33%, and 0.004% for the plate, cylinder, and sphere are obtained, respectively, with this approach.

Green’s Function Partitioning in Galerkin-Based Integral Solution of the Diffusion Equation

1990 ◽  
Vol 112 (1) ◽  
pp. 28-34 ◽  
Author(s):  
A. Haji-Sheikh ◽  
J. V. Beck
Keyword(s):  
Green’S Function ◽  
Green's Function ◽  
Large Time ◽  
Small Time ◽  
Solution Technique ◽  
Heterogeneous Solids ◽  
Function Solution ◽  
Nonhomogeneous Boundary ◽  
Time Partitioning ◽  
Time Accuracy

A procedure to obtain accurate solutions for many transient conduction problems in complex geometries using a Galerkin-based integral (GBI) method is presented. The nonhomogeneous boundary conditions are accommodated by the Green’s function solution technique. A Green’s function obtained by the GBI method exhibits excellent large-time accuracy. It is shown that the time partitioning of the Green’s function yields accurate small-time and large-time solutions. In one example, a hollow cylinder with convective inner surface and prescribed heat flux at the outer surface is considered. Only a few terms for both large-time and small-time solutions are sufficient to produce results with excellent accuracy. The methodology used for homogeneous solids is modified for application to complex heterogeneous solids.

THE LARGE-MATURITY SMILE FOR THE SABR AND CEV-HESTON MODELS

2013 ◽  
Vol 16 (08) ◽  
pp. 1350047 ◽  
Author(s):  
MARTIN FORDE ◽  
ANDREY POGUDIN
Keyword(s):  
Implied Volatility ◽  
Large Time ◽  
Heston Model ◽  
Large Time Asymptotics ◽  
Cev Model ◽  
Constant Elasticity ◽  
Constant Elasticity Of Variance ◽  
Time Estimates ◽  
Time Asymptotics ◽  
Sabr Model

Large-time asymptotics are established for the SABR model with β = 1, ρ ≤ 0 and β < 1, ρ = 0. We also compute large-time asymptotics for the constant elasticity of variance (CEV) model in the large-time, fixed-strike regime and a new large-time, large-strike regime, and for the uncorrelated CEV-Heston model. Finally, we translate these results into a large-time estimates for implied volatility using the recent work of Gao and Lee (2011) and Tehranchi (2009).

scholarly journals mBm-Based Scalings of Traffic Propagated in Internet

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
Ming Li ◽  
Wei Zhao ◽  
Shengyong Chen
Keyword(s):  
Large Time ◽  
Observation Interval ◽  
Small Time ◽  
The Other ◽  
The Internet ◽  
Network Systems ◽  
Local Scaling ◽  
Computer Communications ◽  
Time Scaling ◽  
Computer Scientists

Scaling phenomena of the Internet traffic gain people's interests, ranging from computer scientists to statisticians. There are two types of scales. One is small-time scaling and the other large-time one. Tools to separately describe them are desired in computer communications, such as performance analysis of network systems. Conventional tools, such as the standard fractional Brownian motion (fBm), or its increment process, or the standard multifractional fBm (mBm) indexed by the local Hölder functionH(t)may not be enough for this purpose. In this paper, we propose to describe the local scaling of traffic by usingD(t)on a point-by-point basis and to measure the large-time scaling of traffic by using E[H(t)]on an interval-by-interval basis, where E implies the expectation operator. Since E[H(t)]is a constant within an observation interval whileD(t)is random in general, they are uncorrelated with each other. Thus, our proposed method can be used to separately characterize the small-time scaling phenomenon and the large one of traffic, providing a new tool to investigate the scaling phenomena of traffic.

scholarly journals Fast and accurate calculations for first-passage times in Wiener diffusion models

2019 ◽  
Author(s):  
Danielle Navarro ◽  
Ian Fuss
Keyword(s):  
Probability Density ◽  
Large Time ◽  
Small Time ◽  
Diffusion Models ◽  
First Passage Times ◽  
Response Time Models ◽  
Psychonomic Bulletin ◽  
First Passage ◽  
Perceptual Matching ◽  
Passage Times

We propose a new method for quickly calculating the probability density function for first-passage times in simple Wiener diffusion models, extending an earlier method used by [Van Zandt, T., Colonius, H., &amp; Proctor, R. W. (2000). A comparison of two response-time models applied to perceptual matching. Psychonomic Bulletin &amp; Review, 7, 208–256]. The method relies on the observation that there are two distinct infinite series expansions of this probability density, one of which converges quickly for small time values, while the other converges quickly at large time values. By deriving error bounds associated with finite truncation of either expansion, we are able to determine analytically which of the two versions should be applied in any particular context. The bounds indicate that, even for extremely stringent error tolerances, no more than 8 terms are required to calculate the probability density. By making the calculation of this distribution tractable, the goal is to allow more complex extensions of Wiener diffusion models to be developed.

Application of the Direct Stiffness Method to Plane Problems Involving Large, Time-Dependent Deformations

1966 ◽  
Vol 88 (4) ◽  
pp. 771-776 ◽  
Author(s):  
G. F. Gerstenkorn ◽  
A. S. Kobayashi
Keyword(s):  
Large Time ◽  
Numerical Procedure ◽  
Structural Response ◽  
Small Time ◽  
Time Dependent ◽  
Polar Coordinates ◽  
Structural Problems ◽  
Stiffness Method ◽  
Direct Stiffness ◽  
Creep Deformations

The direct stiffness method is used to formulate a numerical procedure for solving plane structural problems involving large, time-dependent deformations and nonhomogeneous, time-dependent material properties. The stiffness matrix in polar coordinates is derived for the state of plane strain. The nonlinear structural response is incrementally linearized by considering the deformation process to be linear within small time increments. The developed procedure is compared numerically with a known solution of creep deformations in a thick-walled cylinder subjected to internal pressure loading and elevated temperature.

scholarly journals Seismic studies of planet-harbouring stars

2013 ◽  
Vol 9 (S301) ◽  
pp. 353-358
Author(s):  
Sylvie Vauclair
Keyword(s):  
Time Scales ◽  
Large Time ◽  
Large Data ◽  
Precise Determination ◽  
Small Time ◽  
Light Curves ◽  
Stellar Oscillations ◽  
The Past ◽  
Central Stars

AbstractDuring the past decades, stellar oscillations and exoplanet searches were developed in parallel, and the observations were done with the same instruments: radial velocity method, essentially with ground-based instruments, and photometric methods (light curves) from space. The same observational data on one star could lead to planet discoveries at large time scales (days to years) and to the detection of stellar oscillations at small time scales (minutes), such as for the star μ Arae. Since the beginning, it seemed interesting to investigate the differences between stars with and without observed planets. Also, a precise determination of the stellar parameters is important to characterize the detected exoplanets. With the thousands of exoplanet candidates discovered by Kepler, automatic procedures and pipelines are needed with large data bases to characterize the central stars. However, precise asteroseismic studies of well-chosen stars are still important for a deeper insight.

scholarly journals The Small-Time Smile and Term Structure of Implied Volatility under the Heston Model

2012 ◽  
Vol 3 (1) ◽  
pp. 690-708 ◽  
Author(s):  
Martin Forde ◽  
Antoine Jacquier ◽  
Roger Lee
Keyword(s):  
Term Structure ◽  
Implied Volatility ◽  
Small Time ◽  
Heston Model
Sign in / Sign up

Export Citation Format

Share Document