ReturnCertificate: Return Certificate valuation using pricing by duplication

In fCertificates: fCertificates - Basics of Certificates and Structured Products Valuation

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

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

Value

the price (scalar or vector) of the ReturnCertificate

Author(s)

Stefan Wilhelm [e-mail]

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")

fCertificates documentation built on May 2, 2019, 5:50 p.m.