construct_implicit_grid_structure {ragtop}

Structure of implicit numerical integration grid

Description

Infer a reasonable structure for our implicit grid solver based on the voltime, structure constant, and requested grid width in standard deviations.

Usage

construct_implicit_grid_structure(
  tenors,
  M,
  S0,
  K,
  c,
  sigma,
  structure_constant,
  std_devs_width,
  min_z_width = 0
)

Arguments

tenors

Tenors of instruments to be treated on this grid

M

Minimum number of timesteps on this grid

S0

An initial stock price, for setting grid scale

K

An instrument reference stock price, for setting grid scale

c

A continuous stock drift rate

sigma

Volatility of diffusion process (without jumps to default)

structure_constant

The maximum ratio between time intervals dt and the square of space intervals dz^2

std_devs_width

The number of standard deviations, in sigma * sqrt(T) units, to incorporate into the grid

min_z_width

Minimum grid width, in log space

Details

Generally speaking pricing will be good to about 10bp of relative accuracy when the ratio of timesteps to voltime (in annualized units) is over 200.

Cases with pathologically low volatility may go awry (in the sense of yielding ultimately inaccurate PDE solutions), as the structure_constant will force a step in z space much bigger than the width in standard deviations.

Value

A list with elements

T

The maximum time for this grid

dt

Largest permissible timestep size

dz

Distance between space grid points

z0

Center of space grid

z_width

Width in z space

half_N

A misnomer, actually (N-1)/2

N

The number of space points

z

Locations of space points

See Also

Other Implicit Grid Solver: find_present_value(), form_present_value_grid(), infer_conforming_time_grid(), integrate_pde(), iterate_grid_from_timestep(), take_implicit_timestep(), timestep_instruments()