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A stochastic volatility model that captures the joint dynamics of forward rate and its volatility with explicit correlation.
A stochastic volatility model that captures the joint dynamics of forward rate and its volatility with explicit correlation.
Developed by Hagan, Kumar, Lesniewski, and Woodward (2002), the SABR model is the industry standard for interest rate and FX volatility smile interpolation. The model's closed-form asymptotic expansion for the implied volatility reproduces the observed market smile and skew while ensuring no-arbitrage conditions are preserved.
β = 0 recovers normal (Bachelier) volatility; β = 1 recovers lognormal (Black) vol.
Industry standard for swaption and FX vol surface interpolation.
Calibration is two-step: fit σ_atm to ATM vol, then β, ρ, ν to wings.
Options and derivatives are financial contracts whose value derives from an underlying asset. The theory of derivative pricing, beginning with the Black-Scholes-Merton model in 1973, is the central intellectual achievement of modern quantitative finance. The practice of derivative pricing and hedging is the largest single source of employment for quants on the sell-side.
Financial machine learning is the application of supervised, unsupervised, and reinforcement learning methods to financial prediction, classification, and decision problems. The defining methodological constraint is that financial data are serially correlated, not independently and identically distributed, which means that the standard machine learning toolkit must be substantially adapted. The dominant practitioner reference is López de Prado (2018).