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- W3123472901 abstract "Usually, in the Black-Scholes pricing theory the volatility is a positive real parameter. Here we explore what happens if it is allowed to be a complex number. The function for pricing a European option with a complex volatility has essential singularities at zero and infinity. The singularity at zero reflects the put-call parity. Solving for the implied volatility that reproduces a given market price yields not only a real root, but also infinitely many complex roots in a neighbourhood of the origin. The Newton-Raphson calculation of the complex implied volatility has a chaotic nature described by fractals." @default.
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- W3123472901 date "2016-12-06" @default.
- W3123472901 modified "2023-09-27" @default.
- W3123472901 title "Stability of calibration procedures: fractals in the Black-Scholes model" @default.
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- W3123472901 hasPublicationYear "2016" @default.
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