An asymptotic expansion for a Black-Scholes type model

被引：3
|
作者：
Lütkebohmert, E [1 ]
机构：
[1] Univ Bonn, Inst Angew Math, Abt Stockast, D-53115 Bonn, Germany
来源：
BULLETIN DES SCIENCES MATHEMATIQUES | 2004年 / 128卷 / 08期
关键词：
Black-Scholes model; asymptotic expansion; Malliavin calculus; borel summability; small diffusion; Laplace method;
D O I：
10.1016/j.bulsci.2004.02.008
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the Black-Scholes model where we add a perturbation term Sigma(i) epsilon(i)sigma(i) to the model with diffusion coefficient sigma(0)(t). Then we derive an asymptotic expansion for the expected value of an European call option at time t. This is done by applying methods of Malliavin calculus. Borel summability of the derived asymptotic expansion is proven. (C) 2004 Elsevier SAS. All rights reserved.
引用
收藏
页码：661 / 685
页数：25
相关论文
共 50 条
  • [41] A note on Wick products and the fractional Black-Scholes model
    Tomas Björk
    Henrik Hult
    Finance and Stochastics, 2005, 9 : 197 - 209
  • [42] 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
  • [43] ON ROBUSTNESS OF THE BLACK-SCHOLES PARTIAL DIFFERENTIAL EQUATION MODEL
    Mastinsek, Miklavz
    INTERNATIONAL JOURNAL OF THEORETICAL AND APPLIED FINANCE, 2016, 19 (02)
  • [44] 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
  • [45] Black-Scholes定价模型
    李培峦
    张增援
    河南科技大学学报(自然科学版), 2014, 35 (05) : 82 - 86+112
  • [46] Control of the Black-Scholes equation
    David, Claire
    COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2017, 73 (07) : 1566 - 1575
  • [47] An inverse Black-Scholes problem
    Riane, Nizar
    David, Claire
    OPTIMIZATION AND ENGINEERING, 2021, 22 (04) : 2183 - 2204
  • [48] A Black-Scholes user's guide to the Bachelier model
    Choi, Jaehyuk
    Kwak, Minsuk
    Tee, Chyng Wen
    Wang, Yumeng
    JOURNAL OF FUTURES MARKETS, 2022, 42 (05) : 959 - 980
  • [49] On modified Black-Scholes equation
    Ahmed, E
    Abdusalam, HA
    CHAOS SOLITONS & FRACTALS, 2004, 22 (03) : 583 - 587
  • [50] Endogenous stochastic arbitrage bubbles and the Black-Scholes model
    Contreras G, Mauricio
    PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2021, 583
12345