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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
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).
The Merton model was developed to value European-style options on shares of dividend-paying stocks. It is crucial to remember that the Merton model is based on a number of assumptions.