Rough stochastic elasticity of variance and option pricing

被引：8

作者：

Cao, Jiling ^{[1
]}

Kim, Jeong-Hoon ^{[2
]}

Kim, See-Woo ^{[2
]}

Zhang, Wenjun ^{[1
]}

机构：

[1] Auckland Univ Technol, Sch Engn Comp & Math Sci, Dept Math Sci, Private Bag 92006, Auckland 1142, New Zealand

[2] Yonsei Univ, Dept Math, Coll Sci, Seoul 03722, South Korea

来源：

FINANCE RESEARCH LETTERS | 2020年 / 37卷

基金：

新加坡国家研究基金会;

关键词：

Short range correlation; Stochastic elasticity of variance; Fractional Ornstein-Uhlenbeck process; Hurst exponent; Mean reversion;

D O I：

10.1016/j.frl.2019.101381

中图分类号：

F8 [财政、金融];

学科分类号：

0202 ;

摘要：

This study is concerned with the elasticity of variance for risky assets. We show that the elasticity of variance for S&P500 exhibits short-range correlations. By using asymptotic and martingale methods, we obtain a semi-analytical expression for the option price in the two-scale regime where the constant elasticity of variance is perturbed by a smooth and bounded function of a rapid fractional Ornstein-Uhlenbeck process with Hurst exponent within (0, 2 ). The associated 1 implied volatility is presented and discussed. As a result, the scope of Markov stochastic elasticity of variance model is extended to a non-Markov case.

引用

页数：11

共 16 条

[1] Properties of the probability density function of the non-central chi-squared distribution [J].

Andras, Szilard ;

Baricz, Arpad .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2008, 346 (02) :395-402

[2]

[Anonymous], 1999, Appl. Math. Finance

[3]

[Anonymous], 2001, Mathematical methods for foreign exchange: A financial engineer's approach

[4] Hybrid scheme for Brownian semistationary processes [J].

Bennedsen, Mikkel ;

Lunde, Asger ;

Pakkanen, Mikko S. .

FINANCE AND STOCHASTICS, 2017, 21 (04) :931-965

[5] PRICING OF OPTIONS AND CORPORATE LIABILITIES [J].

BLACK, F ;

SCHOLES, M .

JOURNAL OF POLITICAL ECONOMY, 1973, 81 (03) :637-654

[6] Affine fractional stochastic volatility models [J].

F. Comte ;

L. Coutin ;

E. Renault .

Annals of Finance, 2012, 8 (2-3) :337-378

[7]

Cox J., 1975, NOTES OPTION PRICING

[8] Option pricing under fast-varying long-memory stochastic volatility [J].

Garnier, Josselin ;

Solna, Knut .

MATHEMATICAL FINANCE, 2019, 29 (01) :39-83

[9] Option pricing under fast-varying and rough stochastic volatility [J].

Garnier J. ;

Sølna K. .

Annals of Finance, 2018, 14 (4) :489-516

[10] Correction to Black-Scholes Formula Due to Fractional Stochastic Volatility [J].

Garnier, Josselin ;

Solna, Knut .

SIAM JOURNAL ON FINANCIAL MATHEMATICS, 2017, 8 (01) :560-588

← 1 2 →