Black Scholes Model

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Black Scholes Model

A model for mathematically pricing options. The model takes into account the strike price, the time until the expiration date, the price of the underlying asset, and the standard deviation of the underlying asset's return. The model assumes that the option can only be exercised on the expiration date, that it will provide a risk-free return, and that the volatility of the underlying asset will remain constant throughout the life of the contract. The calculation is slightly different for calls and puts. See also: Option Adjusted Spread, Option Pricing Curve.
References in periodicals archive ?
In its raw form, the Black Scholes model is only applicable to non dividend paying European options.
The table contains pricing errors for the Black Scholes and Student models.
Key words: Black Scholes Model, <<classic>> Solution, auxiliary Characteristic <<Psi>>, Conservation Laws.
Sin embargo permanece la dificultad de expandir los conceptos de leyes de conservacion y de la simetria en modelos economicos y financieros, ademas que la idea de la busqueda de leyes de conservacion en el modelo de Black Scholes no es nueva autores como De Leon y Martin de Diego (1997), Ibragimov (1994), Mete (2005), Gazizov e Ibraguimov (1996), Pooe, Mahomed y Waho (2003).
En el modelo de Black Scholes la ecuacion (1) se deduce a partir de un proceso estocastico de tipo de difusion y esta ligada con la ecuacion de difusion.
Pero existen diferencias claras, por ejemplo: a la condicion inicial para la ecuacion de difusion corresponde la condicion final para la ecuacion de Black Scholes ya que la <<difusion>> en el modelo de Black Scholes se hace <<hacia el pasado>>.
Esta ultima transformacion despeja claramente el sentido de ambos parametros de la ecuacion de Black Scholes: [[sigma].sup.2] s representa el coeficiente de difusion constante <<durante dicha difusion inversa>> lo que corresponde a su denominacion volatilidad.
Esto representa una de varias manifestaciones de un papel importante de este parametro en el modelo de Black Scholes; vease tambien la formula (2b).
La solucion <<clasica>> de la ecuacion de Black Scholes es la construccion siguiente vease por ejemplo Wilmott, Howison y Dewynne (1995), Stampfli y Goodman (2001), Sukhomlin y Jacquinot (2006):
Kryzanowski, 1986, "Alternative Specifications of the Errors in the Black Scholes Option-Pricing Model and Various Implied-Variance Formulas", Economics Letters, 21:61-65
Option pricing formulas, such as Black Scholes Merton or the binomial lattice, combine the values associated with the above factors to calculate fair value, using sophisticated mathematics.
The theoretical market value of the share options granted is DKK20.1m, (calculated using the Black Scholes model.