fCertificates (version 0.5-4)

Strangle: Strangle valuation

Description

valuation of a long strangle strategy (one long call + one long put with different strike prices) using pricing by duplication

Usage

Strangle(S, X1, X2, Time, r, r_d, sigma, ratio = 1)

Arguments

S

the asset price, a numeric value or vector.

X1

the exercise price of the long put, a numeric value.

X2

the exercise price of the long call, 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 Strangle

Details

A strangle is a combination of

1. a long put with strike price X1 and
2. a long call with strike price X2 (X1 < X2).

When X1 = X2 the strategy becomes a straddle.

See Also

GBSOption, Straddle

Examples

##
Strangle(S=50, X1=40, X2=60, Time=1, r=0.01, r_d=0, sigma=0.3, ratio=1)

## payoff diagram
S <- 1:100
ps1 <- Strangle(S, X1=45, X2=55, Time=1, r=0.01, r_d=0, sigma=0.3, ratio=1)
ps2 <- Strangle(S, X1=45, X2=55, Time=0, r=0.01, r_d=0, sigma=0.3, ratio=1)
ps3 <- Strangle(S, X1=45, X2=55, 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="Strangle")
lines(S, ps1, col="blue")
lines(S, ps3, col="green")
abline(v=c(45, 55), lty=2, col="gray80")