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

In fCertificates: Basics of Certificates and Structured Products Valuation

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

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)

Value

the price (scalar or vector) of the DiscountCertificate

Author(s)

Stefan Wilhelm [e-mail]

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")

Example output

Loading required package: fBasics
Loading required package: timeDate
Loading required package: timeSeries
Loading required package: fOptions


Rmetrics Package fOptions
Pricing and Evaluating Basic Options
Copyright (C) 2005-2014 Rmetrics Association Zurich
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Loading required package: fExoticOptions
[1] 35.47015

fCertificates documentation built on May 1, 2019, 10:09 p.m.