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Quant Insider on Instagram: "In options pricing, Monte Carlo simulation and PDE methods are often presented as alternative numerical techniques. Mathematically, they are not. When you simulate asset paths under the risk-neutral measure with sufficiently small time steps, you are implicitly defining local increments. If those increments have a well-defined first conditional moment (the risk-neutral drift) and a well-defined second conditional moment (the variance), and higher moments vanish fast
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