SprintCertificate: Sprint Certificate valuation using pricing by duplication

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

Description

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

Usage

SprintCertificate(S, X, Cap, Time, r, r_d, sigma, participation, ratio = 1)

Arguments

S	the asset price, a numeric value.
X	the exercise price, 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.
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

A Sprint Certificate is a combination of

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

2. 2 long calls with strike price X

3. a short call with strike price Cap

The long calls permit an outperformance (double participation) in the range between strike level X and Cap at maturity. It is somehow a capped outperformance certificate.

Alternative names of this structure are:

1. Kick-start-Certificates

2. Double-Chance-Certificate

3. Capped Outperformance Certificate

Classification according to the SVSP Swiss Derivative Map 2008: Capped Outperformance Certificates (350)
Classification according to the SVSP Swiss Derivative Map 2010: Capped Outperformance Certificates (1240)

Value

the price (scalar or vector) of the SprintCertificate

Author(s)

Stefan Wilhelm [e-mail]

References

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

See Also

similar structures: OutperformanceCertificate

Examples

##
SprintCertificate(S=32, X=30, Cap=40, Time=1, r=0.045, 
  r_d=0, sigma=0.4, participation=2, ratio = 1)

## payoff diagramm
S <- seq(0, 100)
p <- SprintCertificate(S, X=30, Cap=40, Time=1, r=0.045, 
  r_d=0, sigma=0.4, participation=2, ratio = 1)  
p2 <- SprintCertificate(S, X=30, Cap=40, Time=0, r=0.045, 
  r_d=0, sigma=0.4, participation=2, ratio = 1)  
plot(S, p,  type="l", col="red", , ylim=range(p, p2, na.rm=TRUE), 
  xlab="underlying price", ylab="payoff", main="Sprint")
lines(S, p2, col="blue")
abline(v=c(30, 40), 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] 32.68324

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