fCertificates (version 0.5-4)

OutperformanceCertificate: Outperformance Certificate valuation using pricing by duplication

Description

values a Outperformance Certificate using pricing by duplication

Usage

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

Arguments

S

the asset price, a numeric value.

X

the exercise price (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 OutperformanceCertificate

Details

A Outperformance Certificate is a combination of

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

The long call permits a outperformance above strike level X. Classification according to the SVSP Swiss Derivative Map 2008: Outperformance Certificates (230) Classification according to the SVSP Swiss Derivative Map 2010: Outperformance Certificates (1310)

References

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

Examples

##
OutperformanceCertificate(S=50, X=60, Time=1, 
  r=0.03, r_d=0, sigma=0.4, participation=1.2, ratio = 1)
    
## payoff diagram
S <- seq(0,100)
p <- OutperformanceCertificate(S, X=60, Time=1, 
  r=0.03, r_d=0, sigma=0.4, participation=1.2, ratio = 1)
p2 <- OutperformanceCertificate(S, X=60, Time=0, 
  r=0.03, r_d=0, sigma=0.4, 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="Outperformance")
lines(S, p2, col="blue")
abline(v=60, lty=2, col="gray80")