fCertificates (version 0.5-4)

ReverseDiscountCertificate: Reverse Discount Certificate valuation using pricing by duplication

Description

values a Reverse Discount certificate using pricing by duplication

Usage

ReverseDiscountCertificate(S, S0, X, Time, r, r_d, sigma, ratio = 1)

Arguments

S

the asset price, a numeric value.

S0

the underlying start price at issue date

X

the exercise price, 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 Reverse Discount Certificate

Details

A Reverse Discount certificate is composed of

1. a short position in stock with reference price S0 (i.e. a Put with strike S0)
2. a short put with strike price X

See Also

similar structures: DiscountCertificate, ReverseDiscountPlusCertificate

Examples

## 
ReverseDiscountCertificate(S=100, S0=100, X=90, Time=1, 
  r=0.045, r_d=0, sigma=0.4, ratio=1)

## payoff diagram
S <- seq(0, 150)
p <- ReverseDiscountCertificate(S, S0=100, X=90, Time=1, 
  r=0.045, r_d=0, sigma=0.4, ratio=1)
p2 <- ReverseDiscountCertificate(S, S0=100, X=90, Time=0, 
  r=0.045, r_d=0, sigma=0.4, ratio=1)
plot(S, p,  type="l", col="red", ylim=range(p, p2, na.rm=TRUE), 
  xlab="underlying price", ylab="payoff", main="Reverse Discount")
lines(S, p2, col="blue")
abline(v=90, lty=2, col="gray80")