fCertificates (version 0.5-4)

Straddle: Straddle valuation

Description

valuation of a long Straddle strategy (one long call + one long put with same strike price) using pricing by duplication

Usage

Straddle(S, X, Time, r, r_d, sigma, ratio = 1)

Arguments

S

the asset price, a numeric value.

X

the exercise price, a numeric value.

Time

time to maturity measured in years

r

the annualized rate of interest, a numeric value; e.g. 0.25 means 25% pa.

r_d

the annualized dividend yield, a numeric value; e.g. 0.25 means 25% pa.

sigma

the annualized volatility of the underlying security, a numeric value; e.g. 0.3 means 30% volatility pa.

ratio

ratio, number of underlyings one certificate refers to, a numeric value; e.g. 0.25 means 4 certificates refer to 1 share of the underlying asset

Value

the price of the Straddle, either scalar or vector

Details

A strangle is a combination of

1. a long put
2. a long call

with the same strike price X. If the strike prices of the 2 options differ (i.e. X1 < X2), then the strategy is called a long strangle.

See Also

GBSOption, Strangle

Examples

S <- seq(0, 100)
prices <- Straddle(S, X=50, Time=0, r=0.05, r_d=0, sigma=0.2, ratio = 1)
plot(S, prices, type="l", xlab="underlying price", ylab="payoff") 
 
## Straddle payoff diagram
S <- seq(0, 100)
ps1 <- Straddle(S, X=45, Time=1, r=0.01, r_d=0, sigma=0.3, ratio=1)
ps2 <- Straddle(S, X=45, Time=0, r=0.01, r_d=0, sigma=0.3, ratio=1)
ps3 <- Straddle(S, X=45, Time=1, r=0.01, r_d=0, sigma=0.4, ratio=1)

plot(S, ps2, type="l", col="red", xlab="underlying price", 
  ylab="payoff", main="Straddle")
lines(S, ps1, col="blue")
lines(S, ps3, col="green")
abline(v=45, lty=2, col="gray80")