Dupire’s Equation, a fundamental partial differential equation in quantitative finance, facilitates the calibration of an implied local volatility surface directly from observed option prices. It provides a model-independent framework for deriving the instantaneous volatility of an asset as a function of its spot price and time to expiry, capturing the market’s forward view of volatility dynamics.
Mechanism
The equation links the observed market prices of European options across various strikes and maturities to a unique local volatility function. Its operation involves solving a Fokker-Planck equation in reverse, where the option price satisfies a backward Kolmogorov equation, thereby extracting the implied diffusion coefficient that makes the model consistent with market quotes, given sufficient liquidity.
Methodology
Within crypto institutional options trading, Dupire’s Equation is employed to construct a consistent local volatility surface, crucial for pricing exotic options and managing complex derivatives portfolios. This methodology provides a practical means to capture the “volatility smile” and “skew” effects observed in crypto options markets, offering a robust tool for risk assessment and hedging strategies without assuming a specific stochastic process for asset price dynamics.
Local volatility offers perfect static calibration, while stochastic volatility provides superior dynamic realism for hedging and pricing complex derivatives.
We use cookies to personalize content and marketing, and to analyze our traffic. This helps us maintain the quality of our free resources. manage your preferences below.
Detailed Cookie Preferences
This helps support our free resources through personalized marketing efforts and promotions.
Analytics cookies help us understand how visitors interact with our website, improving user experience and website performance.
Personalization cookies enable us to customize the content and features of our site based on your interactions, offering a more tailored experience.
