Calculate Black-Scholes option price

Calculate Black-Scholes option price

Usage

BlackScholesPrice(
  strike = forward,
  spot,
  texp = 1,
  sigma,
  intr = 0,
  divr = 0,
  cp = 1L,
  forward = spot * exp(-divr * texp)/df,
  df = exp(-intr * texp)
)

Arguments

strike

(vector of) strike price

spot

(vector of) spot price

texp

(vector of) time to expiry

sigma

(vector of) volatility

intr

interest rate (domestic interest rate)

divr

dividend/convenience yield (foreign interest rate)

cp

call/put sign. 1 for call, -1 for put.

forward

forward price. If given, forward overrides spot

df

discount factor. If given, df overrides intr

Value

option price

References

Black, F., & Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81(3), 637-654. doi:10.1086/260062

Black, F. (1976). The pricing of commodity contracts. Journal of Financial Economics, 3(1), 167-179. doi:10.1016/0304-405X(76)90024-6

https://en.wikipedia.org/wiki/Black-Scholes_model

See also

BlackScholesImpvol

Examples

spot <- 100
strike <- seq(80,125,5)
texp <- 1.2
sigma <- 0.2
intr <- 0.05
FER::BlackScholesPrice(strike, spot, texp, sigma, intr=intr)
#>  [1] 25.535142 21.529004 17.856068 14.568093 11.694956  9.242988  7.197247
#>  [8]  5.526345  4.188286  3.136053