Can There Be an Explicit Formula for Implied Volatility?

نویسنده

  • STEFAN GERHOLD
چکیده

It is “well known” that there is no explicit expression for the Black-Scholes implied volatility. We prove that, as a function of underlying, strike, and call price, implied volatility does not belong to the class of Dfinite functions. This does not rule out all explicit expressions, but shows that implied volatility does not belong to a certain large class, which contains many elementary functions and classical special functions.

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تاریخ انتشار 2012