May 03, 2023
Why do we need an options pricing model?
In 1973, Black and Scholes published The Pricing of Options and Corporate Liabilities, inventing the Black-Scholes Options Pricing Model. One critical element of their model is that the value of an option with the price \(S\), strike \(K\), and maturity \(T\), is dependent on the variance of the underlying stock price.
This makes intuitive sense, the value of a call option is, at some level, a probability-weighted value, based on all possible futures values of the underlying stock price, minus the strike. If the price of the stock is highly volatile, it follows that there is a higher probability that the stock price will end up above the strike price, and therefore valuable to the owner of the option.