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Black model

The Black model (sometimes known as the Black-76 model) is a variant (and more general form) of the Black-Scholes option pricing model. It is widely used in the futures market and interest rate market for pricing options. It was first presented in a paper written by Fischer Black in 1976.

Table of contents
1 The Black formula
2 Derivation and assumptions
3 See also
4 External links
5 References

The Black formula

The Black formula for a call option on an underlying struck at K, expiring T years in the future is

is the risk-free interest rate
is the current forward price of the underlying for the option maturity
is the volatility of the forward price.
and is the standard cumulative Normal distribution function.

The put price is

Derivation and assumptions

The derivation of the pricing formulas in the model follows that of the Black-Scholes model almost exactly. The assumption that the spot price follows a log-normal process is replaced by the assumption that the forward price follows such a process. From there the derivation is identical and so the final formula is the same except that the spot price is replaced by the forward - the forward price represents the expected future value discounted at the risk free rate.

See also

External links