CappedBonusCertificate: Capped Bonus Certificate valuation using pricing by...

In fCertificates: fCertificates - Basics of Certificates and Structured Products Valuation

Description

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

Usage

CappedBonusCertificate(S, X, B, Cap, Time, r, r_d, sigma, ratio = 1, 
  barrierHit=FALSE)

Arguments

S	the asset price, a numeric value
X	the exercise price ("Bonuslevel"), a numeric value.
B	the barrier ("Sicherheitslevel"), a numeric value.
Cap	the cap, 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
barrierHit	flag whether the barrier has already been reached/hit during the lifetime

Details

A Capped Bonus Certificate is a combination of

1. a long position in the stock (aka Zero-Strike Call)

2. a long down-and-out-put with strike price X and barrier B (StandardBarrierOption)

3. a short call with strike price equal to cap

The payoff of similar to the one of BonusCertificate, albeit capped.

Classification according to the SVSP Swiss Derivative Map 2008: Capped Bonus Certificates (380)
Classification according to the SVSP Swiss Derivative Map 2010: Capped Bonus Certificates (1250)

Value

the price (scalar or vector) of the CappedBonusCertificate

Author(s)

Stefan Wilhelm [e-mail]

References

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

See Also

BonusCertificate, CappedReverseBonusCertificate for similar structures

Examples

##
CappedBonusCertificate(S=50, X=60 , B=35, Cap=75, Time=2, sigma=0.14, 
  r=0.02, r_d=0, ratio=1)
   
## payoff diagram
S <- seq(0,120)
p <- CappedBonusCertificate(S, X=60 , B=35, Cap=75, Time=2, sigma=0.14, 
  r=0.02, r_d=0, ratio=1)
p2 <- CappedBonusCertificate(S, X=60 , B=35, Cap=75, Time=0, sigma=0.14, 
  r=0.02, r_d=0, ratio=1)
plot(S, p,  type="l", col="red", ylim=range(p, p2, na.rm=TRUE), 
  xlab="underlying price", ylab="payoff", main="Capped Bonus")
lines(S, p2, col="blue")
abline(v=c(35, 60, 75), 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] 57.563

fCertificates documentation built on May 2, 2019, 5:50 p.m.