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Message: <blockquote data-quote="Daniel Duffy" data-source="post: 246755" data-attributes="member: 607"><p>The nice thing about the Complex Step Method is that it works for all values of h without catastrophic subtraction cancellation errors as with traditional divided differences. You can even take h=1.0e−303 but accuracy has an "ergodic" value around h=1.0e−6 (roughly speaking). If the sensitivity satisfies ODE/SDE/PDE then the whole process is even more robust. In that case we can ensure no-arbitrage by using heavy machinery of maximum principle for PDEs and using monotonic finite difference schemes, for example PDEs for vega, delta  and gamma. This is essentially the CSE method.</p></blockquote><p></p>