fCertificates (version 0.5-4)

CappedBonusCertificate: Capped Bonus Certificate valuation using pricing by duplication

Description

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

Usage

CappedBonusCertificate(S, X, B, Cap, 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.

Cap

the cap, 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 (scalar or vector) of the CappedBonusCertificate

Details

A Capped 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)
3. a short call with strike price equal to cap

The payoff of similar to the one of BonusCertificate, albeit capped.

Classification according to the SVSP Swiss Derivative Map 2008: Capped Bonus Certificates (380) Classification according to the SVSP Swiss Derivative Map 2010: Capped Bonus Certificates (1250)

References

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

See Also

BonusCertificate, CappedReverseBonusCertificate for similar structures

Examples

##
CappedBonusCertificate(S=50, X=60 , B=35, Cap=75, Time=2, sigma=0.14, 
  r=0.02, r_d=0, ratio=1)
   
## payoff diagram
S <- seq(0,120)
p <- CappedBonusCertificate(S, X=60 , B=35, Cap=75, Time=2, sigma=0.14, 
  r=0.02, r_d=0, ratio=1)
p2 <- CappedBonusCertificate(S, X=60 , B=35, Cap=75, Time=0, sigma=0.14, 
  r=0.02, r_d=0, ratio=1)
plot(S, p,  type="l", col="red", ylim=range(p, p2, na.rm=TRUE), 
  xlab="underlying price", ylab="payoff", main="Capped Bonus")
lines(S, p2, col="blue")
abline(v=c(35, 60, 75), lty=2, col="gray80")