Optimal Bump Size for Greeks

Junior Quant · Numerical Implementation

Question

Compute the Black-Scholes delta numerically using a finite-difference bump on the spot price. Compare against the analytic formula. Derive the optimal bump size

h

that minimises the sum of truncation error

O(h^2)

and floating-point cancellation error

O(\varepsilon_{\mathrm{mach}} / h)

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