DiscountCall: Capped Warrant (Discount Call/Discount Put) valuation using...

In fCertificates: Basics of Certificates and Structured Products Valuation

Description

This function values a Capped Warrant (Discount Call/Discount Put) Certificate using pricing by duplication and the Generalized Black/Scholes formula.

Usage

DiscountCall(S, X, Cap, Time, r, r_d, sigma, ratio = 1)
DiscountPut(S, X, Cap, Time, r, r_d, sigma, 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.
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 call is a combination of

1. a long call with strike X

2. a short call with strike Cap

Because of the short call component, the discount call is cheaper than a normal call which allows higher returns. On the other hand, the payoff is capped.

A discount put is a combination of

1. a long put with strike Cap

2. a short put with strike X

Because of the short put, the discount put is cheaper than a normal put which allows higher returns. On the other hand, the payoff is capped.

Also known as:

• Capped Warrant

• Spread Warrant

Classification according to the SVSP Swiss Derivative Map 2008: Spread Warrants (115)

Value

the price (scalar or vector) of the Discount Call(Discount Put)

Author(s)

Stefan Wilhelm [e-mail]

References

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

See Also

GBSOption, DiscountPut

Examples

##
DiscountCall(S=10, X=10, Cap=12, Time=1, r=0.045, r_d=0, sigma=0.2, ratio = 1)

## payoff diagram
S <- seq(0,20, by=0.1)
p <- DiscountCall(S, X=10, Cap=12, Time=1, r=0.045, r_d=0, sigma=0.2, ratio = 1)
p2 <- DiscountCall(S, X=10, Cap=12, Time=0, r=0.045, r_d=0, sigma=0.2, ratio = 1)
plot(S, p,  type="l", col="red", , ylim=range(p, p2, na.rm=TRUE), 
  xlab="underlying price", ylab="payoff", main="Discount Call")
lines(S, p2, col="blue")
abline(v=c(10, 12), 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] 0.7064174

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