fCertificates (version 0.5-4)

CappedReverseBonusCertificate: Capped Reverse Bonus Certificate valuation using pricing by duplication

Description

values a Capped Reverse Bonus certificate using pricing by duplication

Usage

CappedReverseBonusCertificate(S, S0, X, B, Cap, Time, r, r_d,  sigma, ratio = 1, barrierHit=FALSE)

Arguments

S

the asset price, a numeric value.

S0

the underlying start price at issue date

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 CappedReverseBonusCertificate

Details

A Reverse Capped Bonus Certificate is a combination of

1. a short position in stock with reference price S0 (i.e. a Put with strike S0)
2. an up-and-out-call with strike X and barrier B
3. a short put with strike price equal to Cap

See Also

ReverseBonusCertificate, ReverseDiscountCertificate for similar structures

Examples

##
CappedReverseBonusCertificate(S=110, S0=100, X=80, B=120, Cap=70, Time=1, 
  r=0.045, r_d=0, sigma=0.4, ratio = 1)
  
## payoff diagram
S <- seq(0,150)
p <- CappedReverseBonusCertificate(S, S0=100, X=80, B=120, Cap=70, Time=1, 
  r=0.045, r_d=0, sigma=0.4, ratio = 1)
p2 <- CappedReverseBonusCertificate(S, S0=100, X=80, B=120, Cap=70, Time=0, 
  r=0.045, r_d=0, sigma=0.4, ratio = 1)
plot(S, p,  type="l", col="red", ylim=range(p, p2, na.rm=TRUE), 
  xlab="underlying price", ylab="payoff", main="Reverse Capped Bonus")
lines(S, p2, col="blue")
abline(v=c(70, 80, 120), lty=2, col="gray80")