medium · Quantitative Finance
What is the primary reason for using a non-uniform (stretched) grid in finite-difference pricing of barrier options?
- To ensure the tridiagonal coefficient matrix stays symmetric, which simplifies the LU decomposition solver here.
- To place more nodes near the barrier level H and the strike K where the second derivative (Gamma) of the option is highest.
- To allow use of the explicit finite-difference scheme for long-dated options by increasing spacing Δ S near the far boundaries.
- To satisfy the Feller condition for strict variance positivity when using the Heston stochastic volatility model in the pricing PDE.
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