Please use this identifier to cite or link to this item: http://hdl.handle.net/1959.14/137370
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- Title
- On option pricing under a completely random measure via a generalized Esscher transform
- Related
- Insurance mathematics and economics, Vol. 43, Issue 1, (2008), p.99-107
- DOI
- 10.1016/j.insmatheco.2008.03.006
- Publisher
- Elsevier BV
- Date
- 2008
- FoR/RFCD Code(s)
-
140200 Applied Economics
010400 Statistics
- Author/Creator
- Lau, John W
- Author/Creator
- Siu, Tak Kuen
- Description
- In this paper, we develop an option valuation model when the price dynamics of the underlying risky asset is governed by the exponential of a pure jump process specified by a shifted kernel-biased completely random measure. The class of kernel-biased completely random measures is a rich class of jump-type processes introduced in [James, L.F., 2005. Bayesian Poisson process partition calculus with an application to Bayesian Lévy moving averages. Ann. Statist. 33, 1771–1799; James, L.F., 2006. Poisson calculus for spatial neutral to the right processes. Ann. Statist. 34, 416–440] and it provides a great deal of flexibility to incorporate both finite and infinite jump activities. It includes a general class of processes, namely, the generalized Gamma process, which in its turn includes the stable process, the Gamma process and the inverse Gaussian process as particular cases. The kernel-biased representation is a nice representation form and can describe different types of finite and infinite jump activities by choosing different mixing kernel functions. We employ a dynamic version of the Esscher transform, which resembles an exponential change of measures or a disintegration formula based on the Laplace functional used by James, to determine an equivalent martingale measure in the incomplete market. Closed-form option pricing formulae are obtained in some parametric cases, which provide practitioners with a convenient way to evaluate option prices.
- Description
- 9 page(s)
- Subject Keyword
- 140200 Applied Economics
- Subject Keyword
- 010400 Statistics
- Subject Keyword
- Option pricing
- Subject Keyword
- Kernel-biased completely random measures
- Subject Keyword
- Generalized Gamma processes
- Subject Keyword
- Esscher transform
- Subject Keyword
- Laplace functionals
- Resource Type
- journal article
- Organisation
- Macquarie University. Dept. of Actuarial Studies
- Identifier
- http://hdl.handle.net/1959.14/137370
- Identifier
- ISSN:0167-6687
- Identifier
- mq-rm-2009000229
- Language
- eng
- Reviewed
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