Guarantee Certificate valuation using pricing by duplication

Description

values a Guarantee Certificate using pricing by duplication

Usage

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

Arguments

S

the asset price, a numeric value.

X

the exercise price ("Bonuslevel"), 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

nominal

nominal value, e.g. 1000 EUR that is guaranteed; can be the same as S the price of one share

Details

A Guarantee Certificate is a combination of

  1. a zero bond with nominal value "nominal"

  2. a number of long calls ("participation", default 1) with strike price X

The long calls allow for upside participation while the zero bond ensures the nominal value at maturity (hence a guarantee).

Also known as:

  • Capital Protected Certificate

  • Structured Note

Classification according to the SVSP Swiss Derivative Map 2008: Uncapped Capital Protection (410)
Classification according to the SVSP Swiss Derivative Map 2010: Uncapped Capital Protection (1100)

Value

the price (scalar or vector) of the GarantieCertificate

Author(s)

Stefan Wilhelm wilhelm@financial.com

References

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

Examples

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##
GarantieCertificate(S=110, X=90, Time=1, r=0.045, r_d=0, 
  sigma=0.4, participation=0.8, ratio = 1, nominal=110)

## payoff diagram
S <- seq(0, 150)
p <- GarantieCertificate(S, X=90, Time=1, r=0.045, r_d=0, 
  sigma=0.4, participation=0.8, ratio = 1, nominal=110)
p2 <- GarantieCertificate(S, X=90, Time=0, r=0.045, r_d=0, 
  sigma=0.4, participation=0.8, ratio = 1, nominal=110)
plot(S, p,  type="l", col="red", , ylim=range(p, p2, na.rm=TRUE), 
  xlab="underlying price", ylab="payoff", 
  main="Uncapped Capital Protection")
lines(S, p2, col="blue")
abline(v=90, lty=2, col="gray80")    

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