fCertificates (version 0.5-4)

DiscountPlusCertificate: DiscountPlus Certificate valuation using pricing by duplication

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

Value

the price (scalar or vector) of the DiscountPlusCertificate

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)

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")