fCertificates (version 0.5-4)

ReturnCertificate: Return Certificate valuation using pricing by duplication

Description

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

Usage

ReturnCertificate(S, Bonus, S0, B, Cap, Time, r, r_d, sigma, ratio = 1,  barrierHit=FALSE)

Arguments

S

the asset price, a numeric value.

Bonus

the bonus payment/cash rebate in EUR

S0

underlying start price

B

the barrier ("Sicherheitslevel"), 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

barrierHit

flag whether the barrier has already been reached/hit during the lifetime

Value

the price (scalar or vector) of the ReturnCertificate

Details

A Return Certificate is similar to a Bonus Certificate in the way it offers an extra payment ("bonus") under certain conditions. However, while with Bonus Certificates this bonus is a fixed amount is payed in the range B and X, Return certificates pays a bonus on top of the underlying price.

1. a long position in the stock (aka Zero-Strike Call)
2. a long binary down-and-out-cash-or-nothing-put with strike price X and barrier B and cash rebate Bonus (BinaryBarrierOption)
3. a short call with strike equal to Cap

References

see packages fOptions and BinaryBarrierOption in package fExoticOptions

See Also

See also GBSOption in package fOptions, BinaryBarrierOption in package fExoticOptions, BonusCertificate

Examples

##
ReturnCertificate (S=100, S0=91.7, Bonus=11, B=45, Cap=91.7, 
  Time=0, r=0.02, r_d = 0, sigma=0.3, ratio = 1)

## payoff diagram
S <- seq(30,120, by=1)
p <- ReturnCertificate (S, S0=91.7, Bonus=11, B=45, Cap=91.7, 
  Time=0.5, r=0.02, r_d = 0, sigma=0.3, ratio = 1)
p2 <- ReturnCertificate (S, S0=91.7, Bonus=11, B=45, Cap=91.7, 
  Time=0, r=0.02, 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="Return Certificate")
lines(S, p2, col="blue")
abline(v=c(45,91.7), lty=2, col="gray80")