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

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

Gamma describes the rate of change in the Delta; it is the second derivative of the option or portfolio of options with respect to the underlying asset's price.

1	Gamma(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

If abs(Gamma) is large then the Delta is very sensitive to changes in the price of the underlying asset.

The Gamma of the option

This Gamma masks that of package:stats; to use the latter write stats::Gamma()

George Fisher GeorgeRFisher@gmail.com

Hull, 7th edition Ch 17 p 369-373

# Hull, 7th edition Ch 17 p 371,2
library(ustreasuries)
Stock    <- 49     # S_0
Exercise <- 50     # K
Time     <- 20/52  # T
Interest <- 0.05   # r
Yield    <- 0      # q
sigma    <- 0.20

gamma <- Gamma(Stock, Exercise, Time, Interest, Yield, sigma)
round(gamma, 3) # 0.066