fCertificates (version 0.5-2)

AirbagPlusCertificate: Airbag Plus Certificate valuation using pricing by duplication

Description

This function values a Airbag Plus certificate using pricing by duplication and the Generalized Black/Scholes formula.

Usage

AirbagPlusCertificate(S, X, B, B2, Time, r, r_d, sigma, 
    participation, ratio = 1, barrierHit = FALSE)

Arguments

S

the asset price, a numeric value.

X

the exercise price ("Partizipationslevel"), a numeric value.

B

the barrier ("Sicherheitslevel"), a numeric value.

B2

the second barrier ("Bonus-Barriere"), 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.

participation

participation rate/factor above strike level. Defaults to 1.

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

barrierHit

flag whether the barrier has already been reached/hit during the lifetime. Defaults to FALSE.

Value

• the price (scalar or vector) of the AirbagPlusCertificate

Details

An Airbag Certificate is a combination of

1. a fixed component X
2. a long call with strike price X
3. X/B short puts with strike price equal to B.
4. a down-and-out-put with barrier B2

References

SVSP Swiss Derivative Map 2008 http://www.svsp-verband.ch/

See Also

AirbagCertificate

Examples

##
AirbagPlusCertificate(S=100, X=100, B=75, B2=60, Time=0, r=0.045, r_d=0, sigma=0.2, 
  participation=1, ratio=1)
  
## payoff diagram
S <- seq(0,120)
p <- AirbagPlusCertificate(S, X=100, B=75, B2=60, Time=1, r=0.045, r_d=0, sigma=0.2, 
  participation=1, ratio=1)
p2 <- AirbagPlusCertificate(S, X=100, B=75, B2=60, Time=0, r=0.045, r_d=0, sigma=0.2, 
  participation=1, ratio=1)  
plot(S, p, ylim=range(p1, p2, na.rm=TRUE), type="l", col="red", 
  xlab="underlying price", ylab="payoff", main="Airbag Plus")
lines(S, p2, col="blue")  
abline(v=c(60, 75, 100), lty=2, col="gray80")