The Pricing of Contingent Claims in a Multivariate Gamma Distributed Economy
In this paper we establish a Risk Neutral Valuation Relationship and develop a framework for pricing multivariate European-style contingent claims in a discrete-time economy using a multivariate gamma distribution. In our framework, risk neutrality is obtained by using market equilibrium conditions,...
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| Format: | Article |
| Language: | English |
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Centre for EMEA Banking, Finance and Economics, London Metropolitan University
2011
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| Online Access: | https://repository.londonmet.ac.uk/441/1/CentreforEMEABankingFinanceAndEconomicsWorkingPaperSeries%20No.21%2011.pdf |
| _version_ | 1804071529241116672 |
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| author | Vitiello, Luiz Rebelo, Ivonia |
| author_facet | Vitiello, Luiz Rebelo, Ivonia |
| author_sort | Vitiello, Luiz |
| collection | LMU |
| description | In this paper we establish a Risk Neutral Valuation Relationship and develop a framework for pricing multivariate European-style contingent claims in a discrete-time economy using a multivariate gamma distribution. In our framework, risk neutrality is obtained by using market equilibrium conditions, leading to preference-free contingent claim pricing equations. Multivariate contingent claim pricing models are of particular interest when payoffs depend on two or more stochastic variables, such as options to exchange one asset for another, options on mutual funds, and options with a stochastic strike price in general. In our model each underlying stochastic variable depends on a systematic gamma distributed term and on an idiosyncratic one, where the former has a direct impact on the correlation structure of the underlying variables. To illustrate the applicability of our framework, we present multivariate gamma distributed versions of well-known multivariate normally/lognormally distributed contingent claim pricing formulae. The gamma distribution is particularly suitable to price stochastic variables that present implied volatilities that are an increasing function of the strike price. |
| first_indexed | 2024-07-09T03:44:42Z |
| format | Article |
| id | oai:repository.londonmet.ac.uk:441 |
| institution | London Metropolitan University |
| language | English |
| last_indexed | 2024-07-09T03:44:42Z |
| publishDate | 2011 |
| publisher | Centre for EMEA Banking, Finance and Economics, London Metropolitan University |
| record_format | eprints |
| spelling | oai:repository.londonmet.ac.uk:4412018-05-21T11:50:19Z http://repository.londonmet.ac.uk/441/ The Pricing of Contingent Claims in a Multivariate Gamma Distributed Economy Vitiello, Luiz Rebelo, Ivonia 330 Economics In this paper we establish a Risk Neutral Valuation Relationship and develop a framework for pricing multivariate European-style contingent claims in a discrete-time economy using a multivariate gamma distribution. In our framework, risk neutrality is obtained by using market equilibrium conditions, leading to preference-free contingent claim pricing equations. Multivariate contingent claim pricing models are of particular interest when payoffs depend on two or more stochastic variables, such as options to exchange one asset for another, options on mutual funds, and options with a stochastic strike price in general. In our model each underlying stochastic variable depends on a systematic gamma distributed term and on an idiosyncratic one, where the former has a direct impact on the correlation structure of the underlying variables. To illustrate the applicability of our framework, we present multivariate gamma distributed versions of well-known multivariate normally/lognormally distributed contingent claim pricing formulae. The gamma distribution is particularly suitable to price stochastic variables that present implied volatilities that are an increasing function of the strike price. Centre for EMEA Banking, Finance and Economics, London Metropolitan University 2011 Article NonPeerReviewed text en https://repository.londonmet.ac.uk/441/1/CentreforEMEABankingFinanceAndEconomicsWorkingPaperSeries%20No.21%2011.pdf Vitiello, Luiz and Rebelo, Ivonia (2011) The Pricing of Contingent Claims in a Multivariate Gamma Distributed Economy. Centre for EMEA Banking, Finance and Economics Working Paper Series, 2011 (21). pp. 1-24. http://www.londonmet.ac.uk/media/london-metropolitan-university/london-met-documents/faculties/guildhall-faculty-of-business-and-law/cicm/working-papers/CIMC-DP-2014_10.pdf DOI10.2139/ssrn.1746304 |
| spellingShingle | 330 Economics Vitiello, Luiz Rebelo, Ivonia The Pricing of Contingent Claims in a Multivariate Gamma Distributed Economy |
| title | The Pricing of Contingent Claims in a Multivariate Gamma Distributed Economy |
| title_full | The Pricing of Contingent Claims in a Multivariate Gamma Distributed Economy |
| title_fullStr | The Pricing of Contingent Claims in a Multivariate Gamma Distributed Economy |
| title_full_unstemmed | The Pricing of Contingent Claims in a Multivariate Gamma Distributed Economy |
| title_short | The Pricing of Contingent Claims in a Multivariate Gamma Distributed Economy |
| title_sort | pricing of contingent claims in a multivariate gamma distributed economy |
| topic | 330 Economics |
| url | https://repository.londonmet.ac.uk/441/1/CentreforEMEABankingFinanceAndEconomicsWorkingPaperSeries%20No.21%2011.pdf |
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