fCertificates (version 0.5-4)

CappedWarrant: Capped Warrant (Discount Call/Discount Put) valuation using pricing by duplication

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

Value

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

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)

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")