Vectorized Black-Scholes pricing of european-exercise options

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Description

Price options according to the famous Black-Scholes formula, with the optional addition of a jump-to-default intensity and discrete dividends.

Usage

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blackscholes(callput, S0, K, r, time, vola, default_intensity = 0,
  divrate = 0, borrow_cost = 0, dividends = NULL)

Arguments

callput

1 for calls, -1 for puts

S0

initial underlying price

K

strike

r

risk-free interest rate

time

Time from 0 until expiration

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 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. Fixed dividends will be converted to proportional for purposes of this algorithm.

Details

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.

Value

A list with elements

Price

The present value(s)

Delta

Sensitivity to underlying price

Vega

Sensitivity to volatility

See Also

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

Other European Options: black_scholes_on_term_structures, implied_volatilities_with_rates_struct, implied_volatilities, implied_volatility_with_term_struct, implied_volatility

Examples

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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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