Description Usage Arguments Details Value Author(s) References See Also Examples
values a Bonus Pro Certificate using pricing by duplication
1 2 | BonusProCertificate(TypeFlag=c("poB1","pdoB2"), S, X, B, Time, time1 = 0,
r, r_d, sigma, ratio = 1, barrierHit = FALSE)
|
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 |
A Bonus Pro Certificate is a combination of
a long position in the stock (aka Zero-Strike Call)
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 of knock-out.
For time1 = 0 (full-time monitoring), the value of a type "poB1" Bonus Pro equals the value of a standard Bonus certificate.
For time1 = Time (no barrier to be monitored), the value of the type "poB1" Bonus Pro duplicates a Protective Put strategy (except for the dividend payments).
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)
the price (scalar or vector) of the BonusPro Certificate
Stefan Wilhelm wilhelm@financial.com
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
BonusCertificate
, PTSingleAssetBarrierOption
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 | ## payoff diagram
S <- seq(50, 130)
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)
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")
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