Kurtosis in black-scholes model with Garch volatility

被引:0
|
作者
Sheraz, Muhammad [1 ]
Preda, Vasile [2 ]
机构
[1] Department of Financial Engineering, Faculty of Science, Ningbo University, China
[2] Faculty of Mathematics and Computer Science, University of Bucharest, Romania
关键词
Electronic trading - Higher order statistics - Commerce - Investments;
D O I
暂无
中图分类号
学科分类号
摘要
The famous Black-Scholes option pricing model is a mathematical description of financial market and derivative investment instruments [3]. In Black-Scholes model volatility is a constant function, where trading option is indeed risky due to random components such as volatility. The notion of non constant volatility was introduced in GARCH processes [6]. Recently a Black-Scholes model with GARCH volatility has been presented [10]. In this article we derive the kurtosis formula for underlying financial time series using BS-Model with GARCH volatility for the case of at the money option. We present the kurtosis formula in terms of the model's parameters. Also we compare our computational results by using another measure of kurtosis for different values of volatilities.
引用
收藏
页码:205 / 216
相关论文
共 50 条
  • [1] KURTOSIS IN BLACK-SCHOLES MODEL WITH GARCH VOLATILITY
    Sheraz, Muhammad
    Preda, Vasile
    UNIVERSITY POLITEHNICA OF BUCHAREST SCIENTIFIC BULLETIN-SERIES A-APPLIED MATHEMATICS AND PHYSICS, 2016, 78 (01): : 205 - 216
  • [2] Implied volatility in black-scholes model with GARCH volatility
    Sheraz, Muhammad
    Preda, Vasile
    1ST INTERNATIONAL CONFERENCE 'ECONOMIC SCIENTIFIC RESEARCH - THEORETICAL, EMPIRICAL AND PRACTICAL APPROACHES', ESPERA 2013, 2014, 8 : 658 - 663
  • [3] Algorithm for Determining the Volatility Function in the Black-Scholes Model
    Isakov, V. M.
    Kabanikhin, S., I
    Shananin, A. A.
    Shishlenin, M. A.
    Zhang, S.
    COMPUTATIONAL MATHEMATICS AND MATHEMATICAL PHYSICS, 2019, 59 (10) : 1753 - 1758
  • [4] The Instantaneous Volatility and the Implied Volatility Surface for a Generalized Black-Scholes Model
    Takaoka, Koichiro
    Futami, Hidenori
    ASIA-PACIFIC FINANCIAL MARKETS, 2010, 17 (04) : 391 - 436
  • [5] A note on Black-Scholes implied volatility
    Chargoy-Corona, Jesus
    Ibarra-Valdez, Carlos
    PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2006, 370 (02) : 681 - 688
  • [6] Adiabaticity conditions for volatility smile in Black-Scholes pricing model
    L. Spadafora
    G. P. Berman
    F. Borgonovi
    The European Physical Journal B, 2011, 79 : 47 - 53
  • [7] SUBLEADING CORRECTION TO THE ASIAN OPTIONS VOLATILITY IN THE BLACK-SCHOLES MODEL
    Pirjol, Dan
    INTERNATIONAL JOURNAL OF THEORETICAL AND APPLIED FINANCE, 2023,
  • [8] Adiabaticity conditions for volatility smile in Black-Scholes pricing model
    Spadafora, L.
    Berman, G. P.
    Borgonovi, F.
    EUROPEAN PHYSICAL JOURNAL B, 2011, 79 (01): : 47 - 53
  • [9] Excursion to Financial Engineering: Volatility Invariance in the Black-Scholes Model
    Herzberg, Frederik S.
    STOCHASTIC CALCULUS WITH INFINITESIMALS, 2013, 2067 : 55 - 59
  • [10] Reconstruction of the local volatility function using the Black-Scholes model
    Kim, Sangkwon
    Han, Hyunsoo
    Jang, Hanbyeol
    Jeong, Darae
    Lee, Chaeyoung
    Lee, Wonjin
    Kim, Junseok
    JOURNAL OF COMPUTATIONAL SCIENCE, 2021, 51