timestep_instruments function

Take an implicit timestep for all the given instruments

Backwardate grid values for all the given instruments from a set of grid values matched to time t+dt to form a new set of grid value as of time t.

timestep_instruments(
  z,
  prev_grid_values,
  t,
  dt,
  S0,
  instruments,
  stock_level_fcn,
  discount_factor_fcn,
  default_intensity_fcn,
  variance_cumulation_fcn,
  dividends = NULL
)

Arguments

• z: Space grid value morphable to stock prices using stock_level_fcn
• prev_grid_values: A matrix with one column for each instrument and one row for each of the $N$ values of z
• t: Time after this timestep has been taken
• dt: Interval to the end of this timestep
• S0: Time zero price of the base equity
• instruments: Instruments corresponding to layers of the value grid in prev_grid_values
• 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

Returns

Grid values after applying an implicit timestep

See Also

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