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Graphical Representation of Option Price and Sensitivities

Fischer Black was the founder of the Black's model for pricing an option on futures, it was one of the extension and generalization of the Black-Scholes differential equation (1973).
It tries to evaluate a fair value of an option, and if it behaves well then the option's market price will equal the theoretical fair value.
The mathematics of their derivation is quite complex.
Interested readers can find it in the original paper Fischer (1976), and the books by Hull (1993).

The Black's model was developed to value European-style options on commodity futures. It is crucial to remember that the Black's model is based on a number of assumptions.

  1. The distribution of terminal future prices (returns) is lognormal.
  2. The underlying commodity pays storage cost during the life of the option.
  3. There are no arbitrage possibilities.
  4. Transactions cost and taxes are zero.
  5. The risk-free interest rates, the storage cost, and the futures volatility are known functions of time over the life of the option.
  6. There are no penalties for short sales of futures.
  7. The market operates continuously and the future prices follows a continuous I to process.

Pricing Models Page Available is a Swing Java Jar File if you just wish to run the models.