Vega: Vega of a European Option
In grfiv/ustreasuries: Treasury Data Download, Fixed-Income Models and Derivative Analyses

Description Usage Arguments Details Value Note Author(s) References Examples

Vega is the sensitivity of an option price to changes in the volatility of the underlying asset

1	Vega(Stock, Exercise, Time, Interest, Yield, sigma)

`Stock`	S0, the initial stock price
`Exercise`	K, the strike price
`Time`	T, the time to maturity in fractional years
`Interest`	r, the risk-free rate of return
`Yield`	q, the dividend yield
`sigma`	the asset volatility

Vega is not a Greek letter, it is the brightest star in the constellation Lyra

The Vega of the option

if abs(Vega) is large, the option or portolio is very sensitive to changes in the volatility of the underlying asset

George Fisher GeorgeRFisher@gmail.com

Hull, 7th edition ch 17 p373-375

# Hull, 7th edition Ch 17 p 375
library(ustreasuries)
Stock    <- 49     # S_0
Exercise <- 50     # K
Time     <- 20/52  # T
Interest <- 0.05   # r
Yield    <- 0      # q
sigma    <- 0.20

vega <- Vega(Stock, Exercise, Time, Interest, Yield, sigma)

writeLines(paste0("The value of Vega is ", round(vega,1),   "\n",
"Therefore, a 1% change in the volatility from 20% to 21%", "\n",
"will raise the price of the option by this amount:",       "\n",
"1% x ", round(vega,1), " = ", round((0.01 * vega), 3),
", from ", Stock, " to ", Stock+round((0.01 * vega), 3)))