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Linear or non-linear in finite-difference methods

Explain the term Linear or non-linear in finite-difference methods.

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Linear or non-linear: Almost every quant finance models are linear, therefore you can solve for a portfolio of options through solving each contract at a time and adding. Several more modern models are nonlinear. Nonlinear and linear doesn’t make this much difference while you are solving by finite-difference methods. Therefore choosing this method gives you much flexibility in the verity of model you can use.

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