In the domain of derivative pricing, quants are essential due to their expertise in developing and implementing sophisticated mathematical models to determine the fair value of derivative instruments. These financial instruments, which include options, futures, and swaps, derive their value from the performance of underlying assets such as stocks, bonds, commodities, or interest rates. Quants use a variety of advanced mathematical techniques to build pricing models.

They often employ stochastic calculus to model the random behavior of financial markets and partial differential equations (PDEs) to describe the evolution of derivative prices over time. For instance, the Black-Scholes model, a widely used PDE, provides a theoretical estimate of European options' prices. More complex derivatives may require Monte Carlo simulations, which use random sampling to estimate the expected value of an option's payoff by simulating numerous potential future price paths of the underlying asset.