Description Usage Arguments Details Value Author(s) References See Also Examples
This function values a Capped Warrant (Discount Call/Discount Put) Certificate using pricing by duplication and the Generalized Black/Scholes formula.
1 2 | DiscountCall(S, X, Cap, Time, r, r_d, sigma, ratio = 1)
DiscountPut(S, X, Cap, Time, r, r_d, sigma, ratio = 1)
|
S |
the asset price, a numeric value. |
X |
the exercise price, 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 |
A discount call is a combination of
a long call with strike X
a short call with strike Cap
Because of the short call component, the discount call is cheaper than a normal call which allows higher returns. On the other hand, the payoff is capped.
A discount put is a combination of
a long put with strike Cap
a short put with strike X
Because of the short put, the discount put is cheaper than a normal put which allows higher returns. On the other hand, the payoff is capped.
Also known as:
Capped Warrant
Spread Warrant
Classification according to the SVSP Swiss Derivative Map 2008: Spread Warrants (115)
the price (scalar or vector) of the Discount Call(Discount Put)
Stefan Wilhelm wilhelm@financial.com
SVSP Swiss Derivative Map http://www.svsp-verband.ch/map/
1 2 3 4 5 6 7 8 9 10 11 | ##
DiscountCall(S=10, X=10, Cap=12, Time=1, r=0.045, r_d=0, sigma=0.2, ratio = 1)
## payoff diagram
S <- seq(0,20, by=0.1)
p <- DiscountCall(S, X=10, Cap=12, Time=1, r=0.045, r_d=0, sigma=0.2, ratio = 1)
p2 <- DiscountCall(S, X=10, Cap=12, Time=0, r=0.045, r_d=0, sigma=0.2, ratio = 1)
plot(S, p, type="l", col="red", , ylim=range(p, p2, na.rm=TRUE),
xlab="underlying price", ylab="payoff", main="Discount Call")
lines(S, p2, col="blue")
abline(v=c(10, 12), lty=2, col="gray80")
|
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Analysing Markets and calculating Basic Statistics
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Copyright (C) 2005-2014 Rmetrics Association Zurich
Educational Software for Financial Engineering and Computational Science
Rmetrics is free software and comes with ABSOLUTELY NO WARRANTY.
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