AirbagCertificate: Airbag Certificate valuation using pricing by duplication

Description Usage Arguments Details Value Author(s) References Examples

View source: R/Certificates.R

Description

This function values a Airbag Certificate using pricing by duplication and the Generalized Black/Scholes formula.

Usage

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

Arguments

S

the asset price, a numeric value.

X

the exercise price ("Partizipationslevel"), a numeric value.

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.

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

Details

An Airbag Certificate is a combination of

  1. a fixed component X

  2. a long call with strike price X

  3. X/B short puts with strike price equal to B.

Classification according to the SVSP Swiss Derivative Map 2008: Airbag Certificates (240)

Value

the price (scalar or vector) of the AirbagCertificate

Author(s)

Stefan Wilhelm wilhelm@financial.com

References

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

Examples

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##
AirbagCertificate(S=100, X=100, B=75, Time=0, r=0.045, r_d=0, sigma=0.2, 
  participation=1, ratio=1)

## payoff diagram
S <- seq(0,120)
p <- AirbagCertificate(S, X=100, B=75, Time=1, r=0.045, r_d=0, sigma=0.2, 
  participation=1, ratio=1)
p2 <- AirbagCertificate(S, X=100, B=75, Time=0, r=0.045, r_d=0, sigma=0.2, 
  participation=1, ratio=1)
plot(S, p,  type="l", col="red", xlab="underlying price", 
  ylab="payoff", main="Airbag")
lines(S, p2, col="blue")
abline(v=c(75, 100), lty=2, col="gray80")

Example output

Loading required package: fBasics
Loading required package: timeDate
Loading required package: timeSeries


Rmetrics Package fBasics
Analysing Markets and calculating Basic Statistics
Copyright (C) 2005-2014 Rmetrics Association Zurich
Educational Software for Financial Engineering and Computational Science
Rmetrics is free software and comes with ABSOLUTELY NO WARRANTY.
https://www.rmetrics.org --- Mail to: info@rmetrics.org
Loading required package: fOptions


Rmetrics Package fOptions
Pricing and Evaluating Basic Options
Copyright (C) 2005-2014 Rmetrics Association Zurich
Educational Software for Financial Engineering and Computational Science
Rmetrics is free software and comes with ABSOLUTELY NO WARRANTY.
https://www.rmetrics.org --- Mail to: info@rmetrics.org
Loading required package: fExoticOptions
[1] 100

fCertificates documentation built on May 1, 2019, 10:09 p.m.