Direct analysis of implied volatility for European options
We show existence and uniqueness of a strong solution to a linear non-uniformly parabolic equation, which gives the fair price of a normalized European call option. We then provide a direct link between local and implied volatilities in the form of a quasilinear degenerate parabolic partial differential equation. We also establish closed-form asymptotic formulae for the implied volatility near expiry as well as for deep in and out of the money options, using a generalized comparison principle on bounded domains.
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- In Collections
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Electronic Theses & Dissertations
- Copyright Status
- In Copyright
- Material Type
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Theses
- Authors
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Wei, Yan
- Thesis Advisors
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Bates, Peter
- Date
- 2012
- Subjects
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Differential equations, Partial
- Program of Study
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Mathematics
- Degree Level
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Doctoral
- Language
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English
- Pages
- vii, 158 pages
- ISBN
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9781267291004
1267291001
- Permalink
- https://doi.org/doi:10.25335/bwp7-c987