fCertificates (version 0.5-4)

SprintCertificate: Sprint Certificate valuation using pricing by duplication

Description

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

Usage

SprintCertificate(S, X, Cap, Time, r, r_d, sigma, participation, ratio = 1)

Arguments

S

the asset price, a numeric value.

X

the exercise price, 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.

participation

participation rate/factor above 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 SprintCertificate

Details

A Sprint Certificate is a combination of

1. a long position in the stock (aka Zero-Strike Call)
2. 2 long calls with strike price X
3. a short call with strike price Cap

The long calls permit an outperformance (double participation) in the range between strike level X and Cap at maturity. It is somehow a capped outperformance certificate. Alternative names of this structure are:

1. Kick-start-Certificates
2. Double-Chance-Certificate
3. Capped Outperformance Certificate

Classification according to the SVSP Swiss Derivative Map 2008: Capped Outperformance Certificates (350) Classification according to the SVSP Swiss Derivative Map 2010: Capped Outperformance Certificates (1240)

References

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

See Also

similar structures: OutperformanceCertificate

Examples

##
SprintCertificate(S=32, X=30, Cap=40, Time=1, r=0.045, 
  r_d=0, sigma=0.4, participation=2, ratio = 1)

## payoff diagramm
S <- seq(0, 100)
p <- SprintCertificate(S, X=30, Cap=40, Time=1, r=0.045, 
  r_d=0, sigma=0.4, participation=2, ratio = 1)  
p2 <- SprintCertificate(S, X=30, Cap=40, Time=0, r=0.045, 
  r_d=0, sigma=0.4, participation=2, ratio = 1)  
plot(S, p,  type="l", col="red", , ylim=range(p, p2, na.rm=TRUE), 
  xlab="underlying price", ylab="payoff", main="Sprint")
lines(S, p2, col="blue")
abline(v=c(30, 40), lty=2, col="gray80")