Microsoft PowerPoint - PoF.ppt

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The volatility is the only para

meter which can not be directly

observed in the market

Ä

We can either use

ƒ

historical estimation OR

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the “implied volatility”.

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Implied volatility

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One can use the BS formula to ca

lculate the volatility given all

other observed values (including the observed market price of the option). This volatility is then

called the “implied volatility”.

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Unfortunately, there exists no clos

ed form solution for the implied

volatility, i.e. we cannot rewrite

the Black-Scholes pricing formula

to get an expression for the impl

ied volatility. However, one can

use numerical procedures (e.g. Monte Carlo simulations) that provide solutions.

Derivative securities: Options - Black-Scholes modelBlack-Scholes model: Pricing formula