Timestep an implicit integration scheme to numerically integrate
the pricing differential equation for each of the given instruments,
backwardating from time Tmax to time 0.
iterate_grid_from_timestep(
starting_time_step,
time_pts,
z,
S0,
instruments,
stock_level_fcn,
discount_factor_fcn,
default_intensity_fcn,
variance_cumulation_fcn,
dividends = NULL,
grid = NULL,
original_grid_values = as.matrix(grid[1 + starting_time_step, , ])
)The index into time_pts of the first timestep to be emplyed. This must be no larger than the length of time_pts, minus one
Time nodes to be treated on the grid
Space grid value morphable to stock prices using stock_level_fcn
Time zero price of the base equity
A list of instruments to be priced. Each
one must have a strike and a optionality_fcn, as
with GridPricedInstrument and its subclasses.
A function for changing space grid value to stock
prices, with arguments z and t
A function for computing present values to
time t of various cashflows occurring during this timestep, with
arguments T, t
A function for computing default intensity
occurring during this timestep, dependent on time and stock price, with
arguments t, S.
A function for computing total stock variance
occurring during this timestep, with arguments T, t. E.g. with
a constant volatility \(s\) this takes the form \((T-t)s^2\).
A data.frame with columns time, fixed,
and proportional. Dividend size at the given time is
then expected to be equal to fixed + proportional * S / S0
An optional grid into which results at each timestep will
be written. Its size should be at least
(1+starting_time_step, length(z), length(instruments))
Grid values to timestep from
Either a populated grid of present values of derivative prices, or a matrix
of values at the first time point, adapted to z at
each timestep. Time zero value will appear in the first index of any grid.
Other Implicit Grid Solver:
construct_implicit_grid_structure(),
find_present_value(),
form_present_value_grid(),
infer_conforming_time_grid(),
integrate_pde(),
take_implicit_timestep(),
timestep_instruments()