fCertificates (version 0.5-4)

BonusCertificate: Bonus Certificate valuation using pricing by duplication

Description

This function values a Bonus Certificate using pricing by duplication and the Generalized Black/Scholes formula.

Usage

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

Arguments

S

the asset price, a numeric value.

X

the exercise price ("Bonuslevel"), 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.

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

Value

the price of the BonusCertificate

Details

A Bonus Certificate is a combination of

1. a long position in the stock (aka Zero-Strike Call)
2. a long down-and-out-put with strike price X and barrier B (StandardBarrierOption)

Classification according to the SVSP Swiss Derivative Map 2008: Bonus Certificates (220) Classification according to the SVSP Swiss Derivative Map 2010: Bonus Certificates (1320)

References

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

See Also

ReverseBonusCertificate, CappedBonusCertificate for similar structures and StandardBarrierOption in the fExoticOptions package for the down-and-out-put

Examples

##
BonusCertificate(S=50, X=60 , B=35, Time=2, sigma=0.14, r=0.02, r_d=0, ratio=1)
 
## payoff diagram
S <- seq(0,120)
p <- BonusCertificate(S, X=60 , B=35, Time=2, sigma=0.14, r=0.02, r_d=0, ratio=1)
p2 <- BonusCertificate(S, X=60 , B=35, Time=0, sigma=0.14, r=0.02, r_d=0, ratio=1)
plot(S, p,  type="l", col="red", xlab="underlying price", 
  ylab="payoff", main="Bonus")
lines(S, p2, col="blue")
abline(v=c(35, 60), lty=2, col="gray80")