fCertificates (version 0.5-4)

OutperformancePlusCertificate: Outperformance Plus Certificate valuation using pricing by duplication

Description

values a Outperformance Plus Certificate using pricing by duplication

Usage

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

Arguments

S

the asset price, a numeric value.

X

the exercise price, a numeric value.

B

the barrier ("Sicherheitslevel"), 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 OutperformancePlusCertificate

Details

A Outperformance Plus Certificate is a combination of

1. a long position in the stock (aka Zero-Strike Call)
2. a number of long calls ("participation") with strike price X
3. a (partial time) down-and-out-put with strike price X and barrier level B

The long call permits a outperformance above strike level X. The down-and-out-put offers partial protection. Also known as:

• Outperformance Bonus Certificate

Classification according to the SVSP Swiss Derivative Map 2008: Outperformance Bonus Certificates (235) Classification according to the SVSP Swiss Derivative Map 2010: Outperformance Bonus Certificates (1330)

References

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

See Also

similar structures: OutperformanceCertificate

Examples

##
OutperformancePlusCertificate(S=10, X=12, B=7, Time=1, 
  r=0.045, r_d=0, sigma=0.4, participation=1.2, ratio = 1)
 
## payoff diagram
S <- seq(30, 100, by=0.1)
p <- OutperformancePlusCertificate(S, X=60, B=40, Time=1, 
  r=0.045, r_d=0, sigma=0.4, participation=1.2, ratio = 1)
p2 <- OutperformancePlusCertificate(S, X=60, B=40, Time=0, 
  r=0.045, r_d=0, sigma=0.4, participation=1.2, ratio = 1)
plot(S, p,  type="l", col="red", , ylim=range(p, p2, na.rm=TRUE), 
  xlab="underlying price", ylab="payoff", main="Outperformance Bonus")
lines(S, p2, col="blue")
abline(v=c(40, 60), lty=2, col="gray80")