find_present_value: Use a model to estimate the present value of financial...

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

Description

Use a finite difference scheme to form estimates of present values for a variety of stock prices. Once the grid has been created, interpolate to obtain the value of each instrument at the present stock price S0

Usage

find_present_value(
  S0,
  num_time_steps,
  instruments,
  const_volatility = 0.5,
  const_short_rate = 0,
  const_default_intensity = 0,
  override_Tmax = NA,
  discount_factor_fcn = function(T, t, ...) {     exp(-const_short_rate * (T - t)) },
  default_intensity_fcn = function(t, S, ...) {     const_default_intensity + 0 * S },
  variance_cumulation_fcn = function(T, t) {     const_volatility^2 * (T - t) },
  dividends = NULL,
  borrow_cost = 0,
  dividend_rate = 0,
  structure_constant = 2,
  std_devs_width = 3
)

Arguments

S0	An initial stock price, for setting grid scale
num_time_steps	Minimum number of time steps in the grid
instruments	A list of instruments to be priced. Each one must have a strike and a optionality_fcn, as with GridPricedInstrument and its subclasses.
const_volatility	A constant to use for volatility in case variance_cumulation_fcn is not given
const_short_rate	A constant to use for the instantaneous interest rate in case discount_factor_fcn is not given
const_default_intensity	A constant to use for the instantaneous default intensity in case default_intensity_fcn is not given
override_Tmax	A different maximum time on the grid to enforce
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
borrow_cost	Stock borrow cost, affecting the drift rate
dividend_rate	Continuous dividend rate, affecting the drift rate
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

Value

A list of present values, with the same names as instruments

See Also

Other Equity Dependent Default Intensity: fit_to_option_market_df(), fit_variance_cumulation(), form_present_value_grid(), implied_jump_process_volatility()

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

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