fCertificates (version 0.5-4)

BonusProCertificate: Bonus Pro Certificate valuation using pricing by duplication

Description

values a Bonus Pro Certificate using pricing by duplication

Usage

BonusProCertificate(TypeFlag=c("poB1","pdoB2"), S, X, B, Time, time1 = 0,  r, r_d, sigma, ratio = 1, barrierHit = FALSE)

Arguments

TypeFlag

see details below

S

the asset price, a numeric value.

X

the exercise price ("Bonuslevel"), a numeric value.

B

the barrier ("Sicherheitslevel"), a numeric value.

Time

time to maturity measured in years

time1

The start time of barrier monitoring, measured in years. Default value = 0

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 BonusPro Certificate

Details

A Bonus Pro Certificate is a combination of

1. a long position in the stock (aka Zero-Strike Call)
2. a long partial time down-and-out-put with strike price X and barrier B (PTSingleAssetBarrierOption)

It just differs from Bonus Certificates in that it has a partial-time-end barrier. Partial-time-end barrier options have the monitoring period start at an arbitrary date before expiration and end at expiration. For example the barrier is just monitored during the last 3 months prior to maturity. Ceteris paribus, this means a reduced risk of knock-out.

There are two types of "B" options: "B1" is defined such that only a barrier hit or crossed causes the option to be knocked out, and a "B2" is defined such that a down-and-out-put is knocked out as soon as the underlying price is below the barrier.

TypeFlag = "poB1": The barrier of the down-and-out-put is only monitored in [time1, Time] with 0 <= time1="" <="Time" (partial-time="" monitoring)="" instead="" of="" [0,="" time].="" ceteris="" paribus,="" this="" means="" a="" reduced="" risk="" knock-out.="" for="" (full-time="" monitoring),="" the="" value="" type="" "pob1"="" bonus="" pro="" equals="" standard="" certificate.="" (no="" barrier="" to="" be="" monitored),="" duplicates="" protective="" put="" strategy="" (except="" dividend="" payments).<="" p="">

TypeFlag = "pdoB2": The down-and-out-put is knocked out as soon as the underlying price is below the barrier. Classification according to the SVSP Swiss Derivative Map 2008: Bonus Certificates (220) Classification according to the SVSP Swiss Derivative Map 2010: Bonus Certificates (1320)

References

SVSP Swiss Derivative Map 2008 http://www.svsp-verband.ch/ Heynen and Kat (1994). Partial barrier options. The Journal of Financial Engineering, 3, 253--274. Haug (2007). The complete Guide to Option Pricing Formulas, Wiley & Sons, 2nd edition, pp.160

See Also

BonusCertificate, PTSingleAssetBarrierOption

Examples

## payoff diagram
S <- seq(50, 130, by=2)
p1 <- numeric(length(S))
p2 <- numeric(length(S))
for (i in seq(along=S))
{
  p1[i] <- BonusProCertificate(TypeFlag="pdoB2", S=S[i], X=100, B=70, 
     Time=0.5, time1 = 0.25, 
     r=0.01, r_d=0, sigma=0.3, ratio = 1)
  p2[i] <- BonusProCertificate(TypeFlag="pdoB2", S=S[i], X=100, B=70, 
     Time=0, time1 = 0, 
     r=0.01, r_d=0, sigma=0.3, ratio = 1)
}   
plot(S, p1, ylim=range(p1, p2, na.rm=TRUE), type="l", lwd=2, col="red",
  xlab="underlying price", ylab="payoff", main="Bonus Pro Certificate")
lines(S, p2, lwd=2, col="blue")
abline(v=c(70, 100), lty=2, col="gray80")
    
## example: BonusPro vs. Bonus Certificate
S <- seq(50, 130, by=2)
p1 <- numeric(length(S))
p2 <- numeric(length(S))
for (i in seq(along=S))
{
  p1[i] <- BonusProCertificate(TypeFlag="pdoB2", S=S[i], X=100, B=70, 
    Time=1, time1 = 0.75, 
    r=0.01, r_d=0, sigma=0.3, ratio = 1)
  p2[i] <- BonusProCertificate(TypeFlag="pdoB2", S=S[i], X=100, B=70, 
    Time=1, time1 = 0.25, 
    r=0.01, r_d=0, sigma=0.3, ratio = 1)
}
p3 <- BonusCertificate(S=S, X=100, B=70, Time=1, r=0.01, r_d=0, sigma=0.3, ratio = 1)
  
plot(S, S, ylim=range(S, p1, p2, p3), type="l", lwd=2, 
  xlab="underlying price", ylab="payoff", main="Bonus Pro Certificate vs. Bonus Certificate")
lines(S, p1, lwd=2, col="red")
lines(S, p2, lwd=2, col="blue")
lines(S, p3, lwd=2, col="darkgreen")
abline(v=c(70,100), lty=2, col="gray")