fCertificates (version 0.5-4)

DiscountCertificate: Discount Certificate valuation using pricing by duplication using pricing by duplication

Description

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

Usage

DiscountCertificate(S, X, Time, r, r_d, sigma, ratio = 1)

Arguments

S

the asset price, a numeric value.

X

the exercise price (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

Value

the price (scalar or vector) of the DiscountCertificate

Details

A Discount 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)

Also known as:

• Covered Call
• Discountzertifikat Classic

Classification according to the SVSP Swiss Derivative Map 2008: Discount Certificates (310) Classification according to the SVSP Swiss Derivative Map 2010: Discount Certificates (1200)

References

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

See Also

DiscountPlusCertificate for a similar structure and GBSOption

Examples

##
DiscountCertificate(S=40, X=42, Time=1, r=0.035, r_d=0, sigma=0.3, ratio=1)

## payoff diagram
S <- seq(0, 100)
p <- DiscountCertificate(S, X=42, Time=1, r=0.035, r_d=0, sigma=0.3, ratio=1)
p2 <- DiscountCertificate(S, X=42, 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="Discount")
lines(S, p2, col="blue")
abline(v=42, lty=2, col="gray80")