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The pricing of credit default swaps under a generalized mixed fractional Brownian motion

Journal Article


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Abstract


  • In this paper, we consider the pricing of the CDS (credit default swap) under a GMFBM (generalized mixed fractional Brownian motion) model. As the name suggests, the GMFBM model is indeed a generalization of all the FBM (fractional Brownian motion) models used in the literature, and is proved to be able to effectively capture the long-range dependence of the stock returns. To develop the pricing mechanics of the CDS, we firstly derive a sufficient condition for the market modeled under the GMFBM to be arbitrage free. Then under the risk-neutral assumption, the CDS is fairly priced by investigating the two legs of the cash flow involved. The price we obtained involves elementary functions only, and can be easily implemented for practical purpose. Finally, based on numerical experiments, we analyze quantitatively the impacts of different parameters on the prices of the CDS. Interestingly, in comparison with all the other FBM models documented in the literature, the results produced from the GMFBM model are in a better agreement with those calculated from the classical Black-Scholes model. © 2014 Published by Elsevier B.V. All rights reserved.

Authors


Publication Date


  • 2014

Citation


  • He, X. & Chen, W. (2014). The pricing of credit default swaps under a generalized mixed fractional Brownian motion. Physica A: Statistical Mechanics and its Applications, 404 26-33.

Scopus Eid


  • 2-s2.0-84896269588

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=4470&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/3453

Number Of Pages


  • 7

Start Page


  • 26

End Page


  • 33

Volume


  • 404

Abstract


  • In this paper, we consider the pricing of the CDS (credit default swap) under a GMFBM (generalized mixed fractional Brownian motion) model. As the name suggests, the GMFBM model is indeed a generalization of all the FBM (fractional Brownian motion) models used in the literature, and is proved to be able to effectively capture the long-range dependence of the stock returns. To develop the pricing mechanics of the CDS, we firstly derive a sufficient condition for the market modeled under the GMFBM to be arbitrage free. Then under the risk-neutral assumption, the CDS is fairly priced by investigating the two legs of the cash flow involved. The price we obtained involves elementary functions only, and can be easily implemented for practical purpose. Finally, based on numerical experiments, we analyze quantitatively the impacts of different parameters on the prices of the CDS. Interestingly, in comparison with all the other FBM models documented in the literature, the results produced from the GMFBM model are in a better agreement with those calculated from the classical Black-Scholes model. © 2014 Published by Elsevier B.V. All rights reserved.

Authors


Publication Date


  • 2014

Citation


  • He, X. & Chen, W. (2014). The pricing of credit default swaps under a generalized mixed fractional Brownian motion. Physica A: Statistical Mechanics and its Applications, 404 26-33.

Scopus Eid


  • 2-s2.0-84896269588

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=4470&context=eispapers

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers/3453

Number Of Pages


  • 7

Start Page


  • 26

End Page


  • 33

Volume


  • 404