BLACK SCHOLES MODEL

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Graphical Representation of Option Price and Sensitivities

Fischer Black and Myron Scholes were the founders of the Black-Scholes model for pricing an option,
it was one of the most significant accomplishments in financial instruments
It tries to evaluate a fair value of an option.
If the model performs as it should, 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, Black-Scholes (1973), and the books by Hull (1993).

The Black-Scholes model was developed to value European-style options on shares of stocks.
It is crucial to remember that the Black-Scholes model is based on a number of assumptions:

  1. The distribution of asset price follows the lognormal random walk.
  2. The underlying asset pays no dividends during the life of the option.
  3. There are no arbitrage possibilities.
  4. Transactions cost and taxes are zero.
  5. The risk-free interest rate and the asset volatility are known functions of time over the life of the option.
  6. There are no penalties for short sales of stock.
  7. The market operates continuously and the share prices follows a continuous Ito process.

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