Calibrating fractional Vasicek model

被引：1

作者：

Han, Yuecai ^{[1
,2
]}

Li, Nan ^{[1
]}

机构：

[1] Jilin Univ, Math Sch, Changchun 130012, Peoples R China

[2] Jilin Univ, Key Lab Symbol Computat & Knowledge Engn, Minist Educ, Changchun, Peoples R China

来源：

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS | 2023年 / 52卷 / 13期

关键词：

Rough fractional stochastic volatility; fractional Vasicek model; parameter estimation; Hurst index; STOCHASTIC VOLATILITY; PARAMETER-ESTIMATION; ASYMPTOTIC THEORY;

D O I：

10.1080/03610926.2021.1994609

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

In this paper, the estimators for the Hurst parameter and diffusion parameter of a Vasicek model driven by fractional Brownian motion are studied, where the observations are in discrete time. Asymptotic properties of these estimators are proved. Using our methods, the smoothness of volatility process of main financial markets is evaluated, corresponding interval estimations are constructed. Our results imply the existence of roughness phenomenon in volatility process.

引用

页码：4429 / 4443

页数：15

共 28 条

[1]

Benassi A, 1997, REV MAT IBEROAM, V13, P19

[2] SHARP LARGE DEVIATIONS FOR THE FRACTIONAL ORNSTEIN-UHLENBECK PROCESS [J].

Bercu, B. ;

Coutin, L. ;

Savy, N. .

THEORY OF PROBABILITY AND ITS APPLICATIONS, 2011, 55 (04) :575-610

[3]

Brouste A., 2010, Statistical Inference Stochastic Processes, V13, P1, DOI DOI 10.1007/S11203-009-9035-X

[4] Parameter estimation for the discretely observed fractional Ornstein-Uhlenbeck process and the Yuima R package [J].

Brouste, Alexandre ;

Iacus, Stefano M. .

COMPUTATIONAL STATISTICS, 2013, 28 (04) :1529-1547

[5] Berry-Esseen bound for the parameter estimation of fractional Ornstein-Uhlenbeck processes with the hurst parameter H ∈ (0,1/2) [J].

Chen, Yong ;

Li, Ying .

COMMUNICATIONS IN STATISTICS-THEORY AND METHODS, 2021, 50 (13) :2996-3013

[6]

Cheridito P., 2003, Electronic Journal of Probability, V8, P1, DOI [10.1214/EJP.v8-125, DOI 10.1214/EJP.V8-125]

[7]

Coeurjolly J.-P., 2001, Stat. Inference for Stoch. Proc, V4, P199, DOI [DOI 10.1023/A:1017507306245, 10.1023/A:1017507306245]

[8] Long memory in continuous-time stochastic volatility models [J].

Comte, F ;

Renault, E .

MATHEMATICAL FINANCE, 1998, 8 (04) :291-323

[9]

Dupire B., 1994, RISK, V7, P18

[10] The characteristic function of rough Heston models [J].

El Euch, Omar ;

Rosenbaum, Mathieu .

MATHEMATICAL FINANCE, 2019, 29 (01) :3-38

← 1 2 3 →