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**1 - 3**of**3**### Geometric L’evy Process Pricing Model.

- Proceedings of Steklov Mathematical Institute,
, 2002

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### [4] L. Andersen, J. Andreasen, Volatility skews and extensions of the LIBOR market

"... [1] C. Alexander, Principal component analysis of implied volatility and skews, ..."

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[1] C. Alexander, Principal component analysis of implied volatility and skews,

### Barrier Option Pricing by Branching Processes

"... This paper examines the pricing of barrier options when the price of the un-derlying asset is modeled by branching process in random environment (BPRE). We derive an analytical formula for the price of an up-and-out call option, one form of a barrier option. Calibration of the model parameters is pe ..."

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This paper examines the pricing of barrier options when the price of the un-derlying asset is modeled by branching process in random environment (BPRE). We derive an analytical formula for the price of an up-and-out call option, one form of a barrier option. Calibration of the model parameters is performed using market prices of standard call options. Our results show that the prices of bar-rier options that are priced with the BPRE model deviate significantly from those modeled assuming a lognormal process, despite the fact that for standard options, the corresponding differences between the two models are relatively small. Key words: Barrier option, up-and-out call option, Bienayme-Galton-Watson branching process, branching process in random environment