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black-sholes model

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## black-sholes model
<br>
### tl; dr
<br>
* mathematical equations that estimates the theoretical value of derivatives based on other investiment instruments
* widely used to price options contracts
* requires five input variables: the strike price of an option, the current stock price, the time to expiration, the risk-free rate, and the volatility
* it posits that these instruments will have a lognormal distribution of prices following a random walk with constant drift and volatility
* it derives the price of a european-style call option
* assumptions: no dividents are paid out during the life of the options, markets are random, no transaction costs in buying the option, risk-free rate and volatility of the underlying assets are known and constant, the returns of the underlying assets are normally distributed.
<br>
<img width="437" src="https://user-images.githubusercontent.com/1130416/219771677-36198efd-55b3-4729-b7f3-e7660a984140.png">