American Institute of Mathematical Sciences

Advanced
  • Previous Article
    On maximizing the expected terminal utility by investment and reinsurance
  • JIMO Home
  • This Issue
  • Next Article
    Sequential characterization of solutions in convex composite programming and applications to vector optimization
October  2008, 4(4): 783-799. doi: 10.3934/jimo.2008.4.783

A power penalty approach to american option pricing with jump diffusion processes

Kai Zhang 1, , Xiaoqi Yang 2, and  Kok Lay Teo 3,

1. 

Department of Finance, Business School, Shenzhen University, Nanhai Ave 3688, Shenzhen, Guangdong 518060, China
2. 

Department of Applied Mathematics, The Hong Kong Polytechnic University, Kowloon, Hong Kong
3. 

Department of Mathematics and Statistics, Curtin University, G.P.O. Box U1987, Perth, WA 6845

Received  February 2008 Revised  August 2008 Published  November 2008

This paper is devoted to develop a power penalty method for pricing the American option model where the underlying asset is assumed to follow a jump diffusion process. With the help of the linear complementarity problem and variational inequalities, we propose a power penalty approach for a partial integro-differential complementarity problem, which is the mathematical model of pricing the American option with a jump diffusion process. The convergence analysis of the power penalty approach is established. Finally, based on the finite element discretization, a numerical scheme is developed to solve the penalized problem and the numerical tests are designed to illustrate the efficiency of this method.
Keywords: American option pricing, finite element method., penalty method.
Mathematics Subject Classification: Primary: 91B28; Secondary: 35K20, 90C3.
Citation: Kai Zhang, Xiaoqi Yang, Kok Lay Teo. A power penalty approach to american option pricing with jump diffusion processes. Journal of Industrial & Management Optimization, 2008, 4 (4) : 783-799. doi: 10.3934/jimo.2008.4.783
[1]

Kai Zhang, Song Wang. Convergence property of an interior penalty approach to pricing American option. Journal of Industrial & Management Optimization, 2011, 7 (2) : 435-447. doi: 10.3934/jimo.2011.7.435
[2]

Lunji Song, Wenya Qi, Kaifang Liu, Qingxian Gu. A new over-penalized weak galerkin finite element method. Part Ⅱ: Elliptic interface problems. Discrete & Continuous Dynamical Systems - B, 2021, 26 (5) : 2581-2598. doi: 10.3934/dcdsb.2020196
[3]

Wen Chen, Song Wang. A finite difference method for pricing European and American options under a geometric Lévy process. Journal of Industrial & Management Optimization, 2015, 11 (1) : 241-264. doi: 10.3934/jimo.2015.11.241
[4]

Mikhail Dokuchaev, Guanglu Zhou, Song Wang. A modification of Galerkin's method for option pricing. Journal of Industrial & Management Optimization, 2021  doi: 10.3934/jimo.2021077
[5]

Nan Li, Song Wang, Shuhua Zhang. Pricing options on investment project contraction and ownership transfer using a finite volume scheme and an interior penalty method. Journal of Industrial & Management Optimization, 2020, 16 (3) : 1349-1368. doi: 10.3934/jimo.2019006
[6]

Wen Li, Song Wang. Pricing American options under proportional transaction costs using a penalty approach and a finite difference scheme. Journal of Industrial & Management Optimization, 2013, 9 (2) : 365-389. doi: 10.3934/jimo.2013.9.365
[7]

Kun Fan, Yang Shen, Tak Kuen Siu, Rongming Wang. On a Markov chain approximation method for option pricing with regime switching. Journal of Industrial & Management Optimization, 2016, 12 (2) : 529-541. doi: 10.3934/jimo.2016.12.529
[8]

Ying Liu, Yanping Chen, Yunqing Huang, Yang Wang. Two-grid method for semiconductor device problem by mixed finite element method and characteristics finite element method. Electronic Research Archive, 2021, 29 (1) : 1859-1880. doi: 10.3934/era.2020095
[9]

Kai Zhang, Kok Lay Teo. A penalty-based method from reconstructing smooth local volatility surface from American options. Journal of Industrial & Management Optimization, 2015, 11 (2) : 631-644. doi: 10.3934/jimo.2015.11.631
[10]

Cornel M. Murea, H. G. E. Hentschel. A finite element method for growth in biological development. Mathematical Biosciences & Engineering, 2007, 4 (2) : 339-353. doi: 10.3934/mbe.2007.4.339
[11]

Martin Burger, José A. Carrillo, Marie-Therese Wolfram. A mixed finite element method for nonlinear diffusion equations. Kinetic & Related Models, 2010, 3 (1) : 59-83. doi: 10.3934/krm.2010.3.59
[12]

Binjie Li, Xiaoping Xie, Shiquan Zhang. New convergence analysis for assumed stress hybrid quadrilateral finite element method. Discrete & Continuous Dynamical Systems - B, 2017, 22 (7) : 2831-2856. doi: 10.3934/dcdsb.2017153
[13]

Kun Wang, Yinnian He, Yueqiang Shang. Fully discrete finite element method for the viscoelastic fluid motion equations. Discrete & Continuous Dynamical Systems - B, 2010, 13 (3) : 665-684. doi: 10.3934/dcdsb.2010.13.665
[14]

Junjiang Lai, Jianguo Huang. A finite element method for vibration analysis of elastic plate-plate structures. Discrete & Continuous Dynamical Systems - B, 2009, 11 (2) : 387-419. doi: 10.3934/dcdsb.2009.11.387
[15]

So-Hsiang Chou. An immersed linear finite element method with interface flux capturing recovery. Discrete & Continuous Dynamical Systems - B, 2012, 17 (7) : 2343-2357. doi: 10.3934/dcdsb.2012.17.2343
[16]

Donald L. Brown, Vasilena Taralova. A multiscale finite element method for Neumann problems in porous microstructures. Discrete & Continuous Dynamical Systems - S, 2016, 9 (5) : 1299-1326. doi: 10.3934/dcdss.2016052
[17]

Xiu Ye, Shangyou Zhang, Peng Zhu. A weak Galerkin finite element method for nonlinear conservation laws. Electronic Research Archive, 2021, 29 (1) : 1897-1923. doi: 10.3934/era.2020097
[18]

Hao Wang, Wei Yang, Yunqing Huang. An adaptive edge finite element method for the Maxwell's equations in metamaterials. Electronic Research Archive, 2020, 28 (2) : 961-976. doi: 10.3934/era.2020051
[19]

Qingping Deng. A nonoverlapping domain decomposition method for nonconforming finite element problems. Communications on Pure & Applied Analysis, 2003, 2 (3) : 297-310. doi: 10.3934/cpaa.2003.2.297
[20]

Runchang Lin. A robust finite element method for singularly perturbed convection-diffusion problems. Conference Publications, 2009, 2009 (Special) : 496-505. doi: 10.3934/proc.2009.2009.496

2020 Impact Factor: 1.801

Tools

Metrics

  • PDF downloads (65)
  • HTML views (0)
  • Cited by (2)

Other articles
by authors

[Back to Top]

Copyright © 2021 American Institute of Mathematical Sciences