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Graphical Representation of Option Price and Sensitivities
Robert Merton was the founder of the Merton model for pricing
an option on dividend-paying stocks, 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 Merton (1973), and the books by Hull (1993).
Pricing Models Page Available is a Swing Java Jar File if you just wish to run the models.