Imagine you need to price a thousand call options on the same stock, each with a different strike. The stock can jump and have fat tails. Running a Monte Carlo simulation for every strike would take ages. But there is a faster way: switch to the language of frequencies. The whole probability distribution of the future stock price can be captured by a single function, called the characteristic function. Then, using a clever algorithm, you can compute all the option prices in one go. That is what Fourier‑based pricing does.