Price an option according to the famous BlackScholes formula, with the
optional addition of a jumptodefault intensity and discrete dividends. Volatility
and rates may be provided as constants or as 2+ parameter functions with
first argument T
corresponding to maturity and second argument t
corresponding to
model date.
1 2 3 4 5 6 7  black_scholes_on_term_structures(callput, S0, K, time, const_volatility = 0.5,
const_short_rate = 0, const_default_intensity = 0,
discount_factor_fcn = function(T, t, ...) { exp(const_short_rate * (T 
t)) }, survival_probability_fcn = function(T, t, ...) {
exp(const_default_intensity * (T  t)) },
variance_cumulation_fcn = function(T, t) { const_volatility^2 * (T  t)
}, dividends = NULL, borrow_cost = 0, dividend_rate = 0)

callput 
1 for calls, 1 for puts 
S0 
initial underlying price 
K 
strike 
time 
Time from 
const_volatility 
A constant to use for volatility in case 
const_short_rate 
A constant to use for the instantaneous interest rate in case 
const_default_intensity 
A constant to use for the instantaneous default intensity in case 
discount_factor_fcn 
A function for computing present values to
time 
survival_probability_fcn 
A function for probability of survival, with
arguments 
variance_cumulation_fcn 
A function for computing total stock variance
occurring during this timestep, with arguments 
dividends 
A 
borrow_cost 
A continuous rate for stock borrow costs 
dividend_rate 
A continuous rate for dividends and other cashflows such as foreign interest rates 
Any term structures will be converted to equivalent constant arguments by calling
them with the arguments (time, 0)
.
Other Equity Independent Default Intensity: american_implied_volatility
,
american
, 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 European Options: blackscholes
,
implied_volatilities_with_rates_struct
,
implied_volatilities
,
implied_volatility_with_term_struct
,
implied_volatility
1 2 3 4 5 6 7 8 9 10 
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