A yield curve is a useful tool for understanding the state of the market and is often used for valuing financial contracts. There is no one yield curve, there are treasury yield curves (at least one for every country), corporate yield curves (one for each issuing entity), and yield curves tied to particular rates, such as SOFR or €STR.

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.