Question

Explain what difficulties in the modeling of interest rates are overcome by Black’s model?

Answer 1

Black's model also known as Black -76 model was developed by Fisher black in 1976 as an improvement over the 1973 Black scholes model.  Its applied to price European call and put options on future contracts, bond options, Interest rate cap and floors, and swaptions. This makes it an effective model for hedging interest rate risks and maintaining flexibility in financial markets.

The primary goal behind development of this model was to overcome the limitations of black and scholes and present a model which can be used to model pricing. In black's own words the future price of a commodity was described as "the price at which we can agree to buy or sell it at a given time in the future without putting up any money now.”. He also reasoned in favor of equating the total long interest rate in any commodity contract to total short interest rate.

One of the key limitations overcome by this model is that it uses forward prices in modeling the value of a futures option at the time of maturity versus the spot prices Black-Scholes uses. It also assumes that volatility is dependent on time, rather than being held as constant as assumed by the black and scholes model.