DiscountPlusCertificate: DiscountPlus Certificate valuation using pricing by...

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

Description

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

Usage

DiscountPlusCertificate(S, X, B, Time, r, r_d, sigma, ratio = 1, 
  barrierActive = TRUE,
  barrierHit = FALSE)

Arguments

S	the asset price, a numeric value.
X	the exercise price (cap), a numeric value.
B	the barrier level, 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
barrierActive	flag telling whether barrier is currently active (TRUE) or inactive (FALSE). Default value is TRUE.
barrierHit	flag whether the barrier has already been reached/hit during the lifetime

Details

A Discount Plus Certificate is a combination of

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

2. a short call with strike price X (= cap)

3. a long (partial-time) down-and-out-put

also known as:

• Barrier Discount Certificates

Classification according to the SVSP Swiss Derivative Map 2008: Barrier Discount Certificates (320)
Classification according to the SVSP Swiss Derivative Map 2010: Barrier Discount Certificates (1210)

Value

the price (scalar or vector) of the DiscountPlusCertificate

Author(s)

Stefan Wilhelm [e-mail]

References

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

See Also

DiscountCertificate for a similar structure and GBSOption

Examples

##
DiscountPlusCertificate(S=42, X=42, B=30, Time=1, r=0.035, r_d=0, sigma=0.3, ratio=1)

## payoff diagram
S <- seq(0, 100)
p <- DiscountPlusCertificate(S, X=42, B=30, Time=1, r=0.035, r_d=0, sigma=0.3, ratio=1)
p2 <- DiscountPlusCertificate(S, X=42, B=30, Time=0, r=0.035, r_d=0, sigma=0.3, ratio=1)
plot(S, p,  type="l", col="red", , ylim=range(p, p2, na.rm=TRUE), 
  xlab="underlying price", ylab="payoff", main="Barrier Discount")
lines(S, p2, col="blue")
abline(v=c(30, 42), lty=2, col="gray80")

Example output

Loading required package: fBasics
Loading required package: timeDate
Loading required package: timeSeries
Loading required package: fOptions
Loading required package: fExoticOptions
[1] 37.46936

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