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Volume 12, Issue 4
FDMs for the PDEs of Option Pricing Under DEV Models with Counterparty Risk

Jingtang Ma, Yong Chen, Taoshun He & Zhijun Tan

DOI: 10.4208/nmtma.OA-2018-0126

Numer. Math. Theor. Meth. Appl., 12 (2019), pp. 1246-1265.

Published online: 2019-06

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  • Abstract

In this paper we study the option pricing problem under dynamic elasticity of variance (DEV) model with counterparty risk. The counterparty risk induces a drop in the asset price and the asset can still be traded after this default time. There are no explicit solutions for the value function of the options. The value functions are governed by two joint partial differential equations (PDEs) which are connected at the default time. The PDEs are discretized by the finite difference methods (FDMs) and the second-order convergence rates both in time and space are derived. Numerical examples are carried out to verify the convergence results.

  • Keywords

Counterparty risk, CEV models, DEV models, European options, finite difference methods.

  • AMS Subject Headings

35R35, 91G20, 91G60, 91G80

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

mjt@swufe.edu.cn (Jingtang Ma)

  • BibTex
  • RIS
  • TXT
@Article{NMTMA-12-1246, author = {Ma , JingtangChen , YongHe , Taoshun and Tan , Zhijun}, title = {FDMs for the PDEs of Option Pricing Under DEV Models with Counterparty Risk}, journal = {Numerical Mathematics: Theory, Methods and Applications}, year = {2019}, volume = {12}, number = {4}, pages = {1246--1265}, abstract = {

In this paper we study the option pricing problem under dynamic elasticity of variance (DEV) model with counterparty risk. The counterparty risk induces a drop in the asset price and the asset can still be traded after this default time. There are no explicit solutions for the value function of the options. The value functions are governed by two joint partial differential equations (PDEs) which are connected at the default time. The PDEs are discretized by the finite difference methods (FDMs) and the second-order convergence rates both in time and space are derived. Numerical examples are carried out to verify the convergence results.

}, issn = {2079-7338}, doi = {https://doi.org/10.4208/nmtma.OA-2018-0126}, url = {http://global-sci.org/intro/article_detail/nmtma/13223.html} }
TY - JOUR T1 - FDMs for the PDEs of Option Pricing Under DEV Models with Counterparty Risk AU - Ma , Jingtang AU - Chen , Yong AU - He , Taoshun AU - Tan , Zhijun JO - Numerical Mathematics: Theory, Methods and Applications VL - 4 SP - 1246 EP - 1265 PY - 2019 DA - 2019/06 SN - 12 DO - http://doi.org/10.4208/nmtma.OA-2018-0126 UR - https://global-sci.org/intro/article_detail/nmtma/13223.html KW - Counterparty risk, CEV models, DEV models, European options, finite difference methods. AB -

In this paper we study the option pricing problem under dynamic elasticity of variance (DEV) model with counterparty risk. The counterparty risk induces a drop in the asset price and the asset can still be traded after this default time. There are no explicit solutions for the value function of the options. The value functions are governed by two joint partial differential equations (PDEs) which are connected at the default time. The PDEs are discretized by the finite difference methods (FDMs) and the second-order convergence rates both in time and space are derived. Numerical examples are carried out to verify the convergence results.

Ma , JingtangChen , YongHe , Taoshun and Tan , Zhijun. (2019). FDMs for the PDEs of Option Pricing Under DEV Models with Counterparty Risk. Numerical Mathematics: Theory, Methods and Applications. 12 (4). 1246-1265. doi:10.4208/nmtma.OA-2018-0126
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