blackscholes: Vectorized Black-Scholes pricing of european-exercise options

In ragtop: Pricing Equity Derivatives with Extensions of Black-Scholes

Description

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

Usage

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 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()

Examples

blackscholes(callput=-1, S0=100, K=90, r=0.03, time=1, # -1 is a PUT
             vola=0.5, default_intensity=0.07)

Example output

Loading required package: limSolve
Loading required package: futile.logger
Welcome to ragtop.  Logging can be enabled with commands such as
  futile.logger::flog.threshold(futile.logger::INFO, name='ragtop.calibration')
$Price
[1] 15.98374

$Delta
[1] -0.2543956

$Vega
[1] 32.07111

ragtop documentation built on March 26, 2020, 7:28 p.m.