values a Guarantee Certificate using pricing by duplication

1 2 | ```
GarantieCertificate(S, X, Time, r, r_d, sigma,
participation, ratio = 1, nominal)
``` |

`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 |

A Guarantee Certificate is a combination of

a zero bond with nominal value "nominal"

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)

the price (scalar or vector) of the GarantieCertificate

Stefan Wilhelm wilhelm@financial.com

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

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 | ```
##
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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