fCertificates (version 0.5-4)

ReverseBonusCertificate: Reverse Bonus Certificate valuation using pricing by duplication

Description

values a Reverse Bonus Certificate using pricing by duplication

Usage

ReverseBonusCertificate(S, S0, X, B, 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.

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 ReverseBonusCertificate

Details

A Reverse Bonus Certificate is a combination of

1. a short position in the stock with reference price 2*S0 (aka long put with Strike 2*S0)
2. a up-and-out-call with strike X and barrier B (Cash rebate K = 0 for standard barrier options)

Examples

##
ReverseBonusCertificate(S=110, S0=120, X=100, B=140, Time=1, r=0.045, 
  r_d=0, sigma=0.4, ratio=1)

## payoff diagram
S <- seq(0, 150)
p <- ReverseBonusCertificate(S, S0=120, X=100, B=140, Time=0.1, r=0.045, 
  r_d=0, sigma=0.4, ratio=1)
p2 <- ReverseBonusCertificate(S, S0=120, X=100, B=140, 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 Bonus")
lines(S, p2, col="blue")
abline(v=c(100, 140), lty=2, col="gray80")