Description Usage Arguments Value See Also Examples
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.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 | american_implied_volatility(
option_price,
callput,
S0,
K,
time,
const_default_intensity = 0,
survival_probability_fcn = function(T, t, ...) { exp(-const_default_intensity * (T
- t)) },
default_intensity_fcn = function(t, S, ...) { const_default_intensity + 0 * S },
...,
num_time_steps = 30,
structure_constant = 2,
std_devs_width = 5,
relative_tolerance = 1e-04,
max.iter = 100,
max_vola = 4
)
|
option_price |
Option price to match |
callput |
1 for calls, -1 for puts |
S0 |
An initial stock price, for setting grid scale |
K |
strike |
time |
Time from |
const_default_intensity |
A constant to use for the instantaneous default intensity in case |
survival_probability_fcn |
(Implied argument) A function for probability of survival, with
arguments |
default_intensity_fcn |
A function for computing default intensity
occurring at a given time, dependent on time and stock price, with
arguments |
... |
Additional arguments to be passed on to |
num_time_steps |
Minimum number of time steps in the grid |
structure_constant |
The maximum ratio between time intervals |
std_devs_width |
The number of standard deviations, in |
relative_tolerance |
Relative tolerance in instrument price defining the root-finder halting condition |
max.iter |
Maximum number of root-finder iterations allowed |
max_vola |
Maximum volatility to try |
Estimated volatility
implied_volatility_with_term_struct
for implied volatility
of European options under the same conditions, american
for the
underlying pricing algorithm
Other Implied Volatilities:
equivalent_bs_vola_to_jump()
,
equivalent_jump_vola_to_bs()
,
fit_variance_cumulation()
,
implied_jump_process_volatility()
,
implied_volatilities_with_rates_struct()
,
implied_volatilities()
,
implied_volatility_with_term_struct()
,
implied_volatility()
Other Equity Independent Default Intensity:
american()
,
black_scholes_on_term_structures()
,
blackscholes()
,
equivalent_bs_vola_to_jump()
,
equivalent_jump_vola_to_bs()
,
implied_volatilities_with_rates_struct()
,
implied_volatilities()
,
implied_volatility_with_term_struct()
,
implied_volatility()
Other American Exercise Equity Options:
american()
,
control_variate_pairs()
1 2 3 4 5 6 | american_implied_volatility(25,CALL,S0=100,K=100,time=2.2,
const_short_rate=0.03, num_time_steps=5)
df250 = function(t) ( exp(-0.02*t)*exp(-0.03*max(0,t-1.0))) # Simple term structure
df25 = function(T,t){df250(T)/df250(t)} # Relative discount factors
american_implied_volatility(25,-1,100,100,2.2,
discount_factor_fcn=df25, num_time_steps=5)
|
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