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 |
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 put 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
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 | # 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))
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