Black Model

Black Model is another version of the Option Pricing Model of Black-Scholes. The Black-Scholes Model is used for different purposes like determining the value of the bond options, swap options, interest rate caps and interest rate floors.
The Black Model is one of the difficult finance formulae at present, but at the same time, the model is very practical and that is why it is very popular as well. Many parameters of Black Model formulae can be observed in practice.

The difference between the Black Scholes formula and the Black Formula is that the in the Black Formula, the forward price takes the place of the spot price related to the underlying option. The formula is as follows:

c = e – rt *[FN(d1)-KN(d2)]

In this formula, r represents the interest rate that is not related to risk factor.

F is the existing forward cost of the particular underlying for maturity of the option. ‘?’ on the other hand represents the unpredictability of the forward price. N(.) denotes the Normal dispersion activity.
At the same time,
d1 = ln((F/K) + (σσ2T/2)) / σ√T
d2 = d1- σ√T

The Put price formula according to the Black Model is as follows:

p = e−rT * [KN(−d2)−FN(−d1)]

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Last Updated on : 1st July 2013

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