Analog of the Black-Scholes formula for option pricing under conditions of \((B, S, X)\)-incomplete market of securities with jumps (Q2722131)
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scientific article; zbMATH DE number 1617376
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Analog of the Black-Scholes formula for option pricing under conditions of \((B, S, X)\)-incomplete market of securities with jumps |
scientific article; zbMATH DE number 1617376 |
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11 July 2001
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Black-Scholes formula
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Feynman-Kac formula
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random evolution process
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Markov process
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Analog of the Black-Scholes formula for option pricing under conditions of \((B, S, X)\)-incomplete market of securities with jumps (English)
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A \((B, S, X)\)-incomplete securities market with jumps as a jump random evolution process which is a combination of the Itô process in random Markov medium and the geometrical compound Poisson process is considered. For a given model the Black-Scholes equation and formula which describes a price of the European call option under conditions of \((B,S,X)\)-incomplete securities market are derived. The Feynman-Kac formula for random evolution process is derived which is used for deriving equations and formulas.
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