Stochastic processes and financial applications

Stochastic processes provide the mathematical language for describing how asset prices, interest rates, and volatility evolve unpredictably over time, and their application to finance has produced tools — from the Black-Scholes formula to modern jump-diffusion and stochastic volatility models — that underpin the pricing and hedging of trillions of dollars in derivative contracts. Getting these models right has direct consequences for how risk is measured, transferred, and priced across markets. Active research is wrestling with persistent gaps between model assumptions and observed market behavior, such as the fat-tailed jumps in asset returns, the complex feedback between many interacting traders (studied through mean field game frameworks), and the challenge of cleanly estimating volatility when high-frequency data are corrupted by microstructure noise. How to build models that are simultaneously tractable, realistic, and robust to misspecification remains a central open question.

Works

119,449

Total citations

1,542,204

Keywords

Option PricingStochastic CalculusJump DiffusionVolatility ModelingMean Field GamesTerm Structure Models