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

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

Theta is the decay in the value of an option or a portfolio of options as time passes

1	ThetaCall(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

In a delta-neutral portfolio, Theta is a proxy for Gamma

The Theta of the call option

divide by 365 for "per calendar day"; 252 for "per trading day"

George Fisher GeorgeRFisher@gmail.com

Hull, 7th edition ch 17 p367-368

# Hull, 7th edition Ch 17 p 367
library(ustreasuries)
Stock    <- 49     # S_0
Exercise <- 50     # K
Time     <- 20/52  # T
Interest <- 0.05   # r
Yield    <- 0      # q
sigma    <- 0.20

thcall <- ThetaCall(Stock, Exercise, Time, Interest, Yield, sigma)

writeLines(paste0("Theta:            ", round(thcall, 2),     "\n",
                  "per calendar day: ", round(thcall/365, 4), "\n",
                  "per trading day:  ", round(thcall/252, 4)))