Description Usage Arguments Details Value Author(s) References See Also Examples
This function values a DiscountPlus certificate using pricing by duplication and the Generalized Black/Scholes formula.
1 2 3 | DiscountPlusCertificate(S, X, B, Time, r, r_d, sigma, ratio = 1,
barrierActive = TRUE,
barrierHit = FALSE)
|
S |
the asset price, a numeric value. |
X |
the exercise price (cap), a numeric value. |
B |
the barrier level, 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 |
barrierActive |
flag telling whether barrier is currently active (TRUE) or inactive (FALSE). Default value is TRUE. |
barrierHit |
flag whether the barrier has already been reached/hit during the lifetime |
A Discount Plus Certificate is a combination of
a long position in the stock (aka Zero-Strike Call)
a short call with strike price X (= cap)
a long (partial-time) down-and-out-put
also known as:
Barrier Discount Certificates
Classification according to the SVSP Swiss Derivative Map 2008: Barrier Discount Certificates (320)
Classification according to the SVSP Swiss Derivative Map 2010: Barrier Discount Certificates (1210)
the price (scalar or vector) of the DiscountPlusCertificate
Stefan Wilhelm wilhelm@financial.com
SVSP Swiss Derivative Map http://www.svsp-verband.ch/map/
DiscountCertificate
for a similar structure and GBSOption
1 2 3 4 5 6 7 8 9 10 11 | ##
DiscountPlusCertificate(S=42, X=42, B=30, Time=1, r=0.035, r_d=0, sigma=0.3, ratio=1)
## payoff diagram
S <- seq(0, 100)
p <- DiscountPlusCertificate(S, X=42, B=30, Time=1, r=0.035, r_d=0, sigma=0.3, ratio=1)
p2 <- DiscountPlusCertificate(S, X=42, B=30, Time=0, r=0.035, 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="Barrier Discount")
lines(S, p2, col="blue")
abline(v=c(30, 42), lty=2, col="gray80")
|
Loading required package: fBasics
Loading required package: timeDate
Loading required package: timeSeries
Loading required package: fOptions
Loading required package: fExoticOptions
[1] 37.46936
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