Implied volatility of an american option with equity-independent term structures
Implied volatility of an american option with equity-independent term structures
Use the grid solver to generate american option values under a default model with survival probabilities not linked to equity prices. and run them through a bisective root search method until a constant volatility matching the provided option price has been found.
S0: An initial stock price, for setting grid scale
K: strike
time: Time from 0 until expiration
const_default_intensity: A constant to use for the instantaneous default intensity in case default_intensity_fcn
is not given
survival_probability_fcn: (Implied argument) A function for probability of survival, with arguments T, t and T>t.
default_intensity_fcn: A function for computing default intensity occurring at a given time, dependent on time and stock price, with arguments t, S. Should be matched to survival_probability_fcn
...: Additional arguments to be passed on to implied_volatility_with_term_struct
and american
num_time_steps: Minimum number of time steps in the grid
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
relative_tolerance: Relative tolerance in instrument price defining the root-finder halting condition
max.iter: Maximum number of root-finder iterations allowed
implied_volatility_with_term_struct for implied volatility of European options under the same conditions, american for the underlying pricing algorithm