Local Volatility Surfaces represent a three-dimensional model illustrating implied volatility as a function of both strike price and time to expiration for an underlying asset. Crucially, this model explicitly accounts for volatility’s dependence on the underlying asset’s price level at any given moment. This is a critical tool for precise pricing and risk management of crypto options.
Mechanism
Unlike simpler implied volatility surfaces, a local volatility surface derives a unique instantaneous volatility for each combination of underlying asset price and time, consistent with observed market option prices. It is typically constructed through a non-parametric inversion of market prices, often using Dupire’s formula. This process creates a smooth, arbitrage-free surface that accurately reflects market dynamics.
Methodology
Its application is central to accurately pricing exotic options and managing the dynamic hedging of complex derivatives positions in volatile crypto markets. The strategic principle involves using this surface to predict how implied volatility changes with the underlying asset’s price. This enables more precise delta, gamma, and vega hedging, providing a robust risk assessment superior to models assuming constant or stochastic volatility.
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