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A new closed-form formula for pricing European options under a skew Brownian motion

Journal Article


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Abstract


  • In this paper, we present a new pricing formula based on a modified Black–Scholes (B-S) model with the standard Brownian motion being replaced by a particular process constructed with a special type of skew Brownian motions. Although Corns and Satchell [2007. “Skew Brownian Motion and Pricing European Options.” The European Journal of Finance 13 (6): 523–544] have worked on this model, the results they obtained are incorrect. In this paper, not only do we identify precisely where the errors in Although Corns and Satchell [2007. “Skew Brownian Motion and Pricing European Options”. The European Journal of Finance 13 (6): 523–544] are, we also present a new closed-form pricing formula based on a newly proposed equivalent martingale measure, called ‘endogenous risk neutral measure’, by which only endogenous risks should and can be fully hedged. The newly derived option pricing formula takes the B-S formula as a special case and it does not induce any significant additional burden in terms of numerically computing option values, compared with the effort involved in computing the B-S formula.

Publication Date


  • 2018

Citation


  • Zhu, S. & He, X. (2018). A new closed-form formula for pricing European options under a skew Brownian motion. The European Journal of Finance, 24 (12), 1063-1074.

Scopus Eid


  • 2-s2.0-85020533702

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1532&context=eispapers1

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/531

Has Global Citation Frequency


Number Of Pages


  • 11

Start Page


  • 1063

End Page


  • 1074

Volume


  • 24

Issue


  • 12

Place Of Publication


  • United Kingdom

Abstract


  • In this paper, we present a new pricing formula based on a modified Black–Scholes (B-S) model with the standard Brownian motion being replaced by a particular process constructed with a special type of skew Brownian motions. Although Corns and Satchell [2007. “Skew Brownian Motion and Pricing European Options.” The European Journal of Finance 13 (6): 523–544] have worked on this model, the results they obtained are incorrect. In this paper, not only do we identify precisely where the errors in Although Corns and Satchell [2007. “Skew Brownian Motion and Pricing European Options”. The European Journal of Finance 13 (6): 523–544] are, we also present a new closed-form pricing formula based on a newly proposed equivalent martingale measure, called ‘endogenous risk neutral measure’, by which only endogenous risks should and can be fully hedged. The newly derived option pricing formula takes the B-S formula as a special case and it does not induce any significant additional burden in terms of numerically computing option values, compared with the effort involved in computing the B-S formula.

Publication Date


  • 2018

Citation


  • Zhu, S. & He, X. (2018). A new closed-form formula for pricing European options under a skew Brownian motion. The European Journal of Finance, 24 (12), 1063-1074.

Scopus Eid


  • 2-s2.0-85020533702

Ro Full-text Url


  • http://ro.uow.edu.au/cgi/viewcontent.cgi?article=1532&context=eispapers1

Ro Metadata Url


  • http://ro.uow.edu.au/eispapers1/531

Has Global Citation Frequency


Number Of Pages


  • 11

Start Page


  • 1063

End Page


  • 1074

Volume


  • 24

Issue


  • 12

Place Of Publication


  • United Kingdom