The Finite Difference Method is a numerical technique employed to approximate solutions to differential equations by replacing derivatives with finite differences. In quantitative finance, it is a primary tool for valuing complex derivatives and managing risk, particularly for crypto options and structured products.
Mechanism
This method discretizes the continuous domain of a differential equation, such as an option pricing PDE, into a grid of discrete points. At each point, the derivatives are approximated using algebraic expressions involving neighboring grid values, transforming the PDE into a solvable system of linear algebraic equations that can be solved iteratively.
Methodology
The strategic utility lies in its ability to price derivatives for which closed-form analytical solutions are unavailable, such as American options or options with early exercise features on crypto assets. This provides a systematic framework for calculating fair values and sensitivities, enabling accurate risk management for institutional crypto options trading.
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