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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 1976.1 The Black formula
The Black formula for a call option on an underlying struck at K, expiring T years in the future is
-
where
- 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
-
2 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.
3 See also
4 External links
5 References
- Black, Fischer (1976). The pricing of commodity contracts, Journal of Financial Economics, 3, 167-179.
- Garman, Mark B. and Steven W. Kohlhagen (1983). Foreign currency option values, Journal of International Money and Finance, 2, 231-237.
Financial mathematics
