On martingale diffusions describing the ‘smile-effect’ for implied volatilities
✍ Scribed by Hans-Jochen Bartels
- Publisher
- John Wiley and Sons
- Year
- 2000
- Tongue
- English
- Weight
- 94 KB
- Volume
- 16
- Category
- Article
- ISSN
- 1524-1904
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✦ Synopsis
This paper discusses di!usion models describing the &smile-e!ect' of implied volatilities for option prices partly following the new approach of Bruno Dupire. If one restricts to the time homogeneous case, a careful study of this approach shows that the call option prices considered as a function of the price x of the underlying security, remaining time to maturity ¹}t and strike price K have necessarily to satisfy a certain functional equation, in order to "t into a coherent model. It is shown that for certain examples of empirically observed option prices which are reported in the literature, this functional equation does not hold.