Generates a modified coefficient matrix (M-matrix) used in the finite difference method from the option inputs. See Tavella and Randall (2000) for more on the standard formulation of the M-matrix.
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S |
list containing the vectors of spatial grid points associated with each underlying. Vector sizes of underlying spatial grid points need not be equal. |
rf |
scalar; applicable risk-free rate (domestic risk-free rate). |
q |
vector; holding costs of the option's underlyings (dividends, foreign risk-free rates, etc.). |
vol |
vector; volatilities of the option's underlyings. |
rho |
matrix; correlation matrix of the option's underlyings. |
matrixFDM
first constructs the non-zero diagonals of the M-matrix and stores them as columns. The bandSparse
function from the Matrix package then constructs a sparse banded matrix from the columns of the previously contructed matrix. Spatial domain boundaries are calculated first-order inwards with second difference terms dropped, maintaining block tridiagonality.
matrixFDM
returns a CsparseMatrix
-class matrix used for timestepping in the finite difference method.
Michael Eichenberger and Carlo Rosa
Tavella, D., Randall, C., 2000. Pricing Financial Instruments: The Finite Difference Method. John Wiley & Sons, Inc., New York.
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