fCertificates (version 0.5-4)

TwinWinCertificate: Twin Win Certificate valuation using pricing by duplication

Description

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

Usage

TwinWinCertificate(S, X, B, Time, r, r_d, sigma,  participation = 1, ratio = 1)

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.

participation

participation rate/factor between bonus level and 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

Value

the price (scalar or vector) of the Twin Win Certificate

Details

A Twin Win Certificate is a combination of

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

The structure is similar to a Bonus Certificate, the only difference is a double participation at maturity in the range between B and X, implying a "Twin Win" situation for slightly falling underlying prices. Classification according to the SVSP Swiss Derivative Map 2008: Twin-Win Certificates (250) Classification according to the SVSP Swiss Derivative Map 2010: Twin-Win Certificates (1340)

References

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

See Also

BonusCertificate for a similar structure

Examples

##
TwinWinCertificate(S=100, X=100, B=80, Time=2, r = 0.03, r_d = 0, 
  sigma=0.15, participation=1.2, ratio = 1)
 
## payoff diagram
S <- seq(50, 150, by=0.1)
p <- TwinWinCertificate(S, X=100, B=80, Time=0.2, r = 0.03, r_d = 0, 
  sigma=0.15, participation=1.2, ratio = 1)
p2 <- TwinWinCertificate(S, X=100, B=80, Time=0, r = 0.03, r_d = 0, 
  sigma=0.15, 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="Twin-Win")
lines(S, p2, col="blue")    
abline(v=c(80, 100), lty=2, col="gray80")