Easy Express Certificate valuation using pricing by duplication

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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

  1. A zero bond/cash component that pays S0 at maturity

  2. A short cash-or-nothing put (CashOrNothingOption) with strike B and cash rebate S0-B

  3. A 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

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##
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")  

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