# Easy Express Certificate valuation using pricing by duplication

### Description

values a Easy Express Certificate using pricing by duplication

### Usage

1 | ```
EasyExpressCertificate(S, S0, B, Time, r, r_d, sigma, ratio = 1)
``` |

### Arguments

`S` |
the asset price, a numeric value. |

`S0` |
the fix amount payed at maturity if underlying is above B |

`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. |

`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 |

### Details

There are more than one duplication of an Easy Express Certificate. One is a combination of

A zero bond/cash component that pays S0 at maturity

A short cash-or-nothing put (

`CashOrNothingOption`

) with strike B and cash rebate S0-BA short plain vanilla put with strike price B

Also known as:

Zanonia-Easy-Zertifikat

Classification according to the SVSP Swiss Derivative Map 2008: Express Certificates (360)

Classification according to the SVSP Swiss Derivative Map 2010: Express Certificates (1260)

### Value

the price (scalar or vector) of the EasyExpressCertificate

### Author(s)

Stefan Wilhelm wilhelm@financial.com

### References

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

### See Also

`CashOrNothingOption`

in fExoticOptions package

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 | ```
##
EasyExpressCertificate(S=80, S0=100, B=70, Time=1,
r=0.045, r_d=0, sigma=0.4, ratio = 1)
## payoff diagramm
S <- seq(0, 140)
p <- EasyExpressCertificate(S, S0=100, B=70, Time=1,
r=0.045, r_d=0, sigma=0.4, ratio = 1)
p2 <- EasyExpressCertificate(S, S0=100, B=70, Time=0,
r=0.045, r_d=0, sigma=0.4, ratio = 1)
plot(S, p, type="l", col="red", , ylim=range(p, p2, na.rm=TRUE),
xlab="underlying price", ylab="payoff", main="Easy Express")
lines(S, p2, col="blue")
abline(v=70, lty=2, col="gray80")
``` |