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F# for Quantitative Finance by Johan Astborg

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Learning the Black-Scholes formula

The Black-Scholes formula was developed by Fischer Black and Myron Scholes in the 1970s. The Black-Scholes formula is a stochastic partial differential equation which estimates the price of an option. The main idea behind the formula is the delta neutral portfolio. They created the theoretical delta neutral portfolio to reduce the uncertainty involved.

This was a necessary step to be able to come to the analytical formula, which we'll cover in this section. The following are the assumptions made under the Black-Scholes formula:

  • No arbitrage
  • Possible to borrow money at a constant risk-free interest rate (throughout the holding of the option)
  • Possible to buy, sell, and shortlist fractional amounts of underlying assets ...

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