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A volatility surface model where instantaneous volatility is a deterministic function of spot price and time.
A volatility surface model where instantaneous volatility is a deterministic function of spot price and time.
Introduced by Bruno Dupire in 1994, the local volatility model calibrates a function σ(S, t) to exactly reproduce the observed market implied volatility surface. It provides a complete, arbitrage-free diffusion model but cannot match the realistic dynamics of forward smile dynamics under stochastic volatility.
Recovers vanilla option prices exactly by construction.
Cannot match the observed forward smile dynamics (the forward smile is too flat).
Commonly used as a base model for exotics before stochastic vol overlay.
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).