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Explain number of dimensions in finite-difference methods

Explain the term number of dimensions in finite-difference methods.

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Number of dimensions: Is there any strong path dependence within the payoff? Is the contract an option at a single underlying or various? Answers to such questions will find out the number of dimensions in the problem. At the extremely least we will have two dimensions: asset (S or r), and time (t). Finite-difference methods cope very well with smaller no. of dimensions, up to four, as. Above that they get quite time consuming.

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