iterate_grid_from_timestep: Iterate over a set of timesteps to integrate the pricing...

In brianboonstra/ragtop: Pricing Equity Derivatives with Extensions of Black-Scholes

Description

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.

Usage

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, , ])
)

Arguments

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_pts	Time nodes to be treated on the grid
z	Space grid value morphable to stock prices using stock_level_fcn
S0	Time zero price of the base equity
instruments	A list of instruments to be priced. Each one must have a strike and a optionality_fcn, as with GridPricedInstrument and its subclasses.
stock_level_fcn	A function for changing space grid value to stock prices, with arguments z and t
discount_factor_fcn	A function for computing present values to time t of various cashflows occurring during this timestep, with arguments T, t
default_intensity_fcn	A function for computing default intensity occurring during this timestep, dependent on time and stock price, with arguments t, S.
variance_cumulation_fcn	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.
dividends	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
grid	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))
original_grid_values	Grid values to timestep from

Value

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.

See Also

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()

brianboonstra/ragtop documentation built on March 7, 2020, 2:23 p.m.