ThetaPut: Theta of a European Put Option

In grfiv/ustreasuries: Treasury Data Download, Fixed-Income Models and Derivative Analyses

Description

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

Usage

ThetaPut(Stock, Exercise, Time, Interest, Yield, sigma)

Arguments

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

Details

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

Value

The Theta of the put option

Note

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

Author(s)

George Fisher [e-mail]

References

Hull, 7th edition ch 17 p367-368

Examples

# 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)
thput  <- ThetaPut(Stock, Exercise, Time, Interest, Yield, sigma)

rKe    <- Interest * Exercise * exp(-Interest*Time)

writeLines(paste0("ThetaCall:        ", round(thcall, 2), "\n",
                  "ThetaPut:         ", round(thput, 2),   "\n",
                  "per calendar day: ", round(thput/365, 4), " (put)", "\n",
                  "per trading day:  ", round(thput/252, 4), " (put)", "\n\n",
    "ThetaPut is always greater than ThetaCall by an amount rKe:", "\n",
    "Diff: ",thput-thcall,"\n",
    "rKe:  ",rKe))

grfiv/ustreasuries documentation built on May 17, 2019, 8:36 a.m.