Description Usage Arguments Details Value See Also Examples
Price options according to the famous Black-Scholes formula, with the optional addition of a jump-to-default intensity and discrete dividends.
1 2 3 4 5 6 7 8 9 10 11 12 | blackscholes(
callput,
S0,
K,
r,
time,
vola,
default_intensity = 0,
divrate = 0,
borrow_cost = 0,
dividends = NULL
)
|
callput |
1 for calls, -1 for puts |
S0 |
initial underlying price |
K |
strike |
r |
risk-free interest rate |
time |
Time from |
vola |
Default-free volatility of the underlying |
default_intensity |
hazard rate of underlying default |
divrate |
A continuous rate for dividends and other cashflows such as foreign interest rates |
borrow_cost |
A continuous rate for stock borrow costs |
dividends |
A |
Note that if the default_intensity
is set larger than zero then
put-call parity still holds. Greeks are reduced according to cumulated default
probability.
All inputs must either be scalars or have the same nonscalar shape.
A list with elements
Price
The present value(s)
Delta
Sensitivity to underlying price
Vega
Sensitivity to volatility
Other European Options:
black_scholes_on_term_structures()
,
implied_volatilities_with_rates_struct()
,
implied_volatilities()
,
implied_volatility_with_term_struct()
,
implied_volatility()
Other Equity Independent Default Intensity:
american_implied_volatility()
,
american()
,
black_scholes_on_term_structures()
,
equivalent_bs_vola_to_jump()
,
equivalent_jump_vola_to_bs()
,
implied_volatilities_with_rates_struct()
,
implied_volatilities()
,
implied_volatility_with_term_struct()
,
implied_volatility()
1 2 | blackscholes(callput=-1, S0=100, K=90, r=0.03, time=1, # -1 is a PUT
vola=0.5, default_intensity=0.07)
|
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