AirbagCertificate: Airbag Certificate valuation using pricing by duplication

In fCertificates: Basics of Certificates and Structured Products Valuation

Description

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

Usage

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 [e-mail]

References

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

Examples

##
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: [e-mail]
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: [e-mail]
Loading required package: fExoticOptions
[1] 100

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