Description Usage Arguments Details Value Author(s) References See Also Examples
View source: R/ExpressCertificates.R
Pricing of Classic Express Certificates using the truncated multivariate normal distribution (early stop probabilities) and numerical integration of the one-dimensional marginal return distribution at maturity
1 2 | ExpressCertificate.Classic(S, X, T, K, g = function(S_T) {S_T},
r, r_d, sigma, ratio = 1)
|
S |
the asset price, a numeric value |
X |
a vector of early exercise prices ("Bewertungsgrenzen"), , vector of length (n-1) |
T |
a vector of evaluation times measured in years ("Bewertungstage"), vector of length n |
K |
vector of fixed early cash rebates in case of early exercise, length (n-1) |
g |
a payoff function at maturity, by default |
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 |
The principal feature inherent to all express certificates is the callable feature with pretermined valuation dates (t_1< … < t_n) prior to final maturity t_n. Express certificates are typically called, if the underlying price on the valuation date is above a strike price (call level): S(t_i) > X(t_i).
The payoff of an express classic certificate at maturity is the underlying performance itself. So the payoff function at maturity takes the simple form of g(S(t_n)) = S(t_n).
We compute early redemption probabilities via the truncated multivariate normal distribution and integrate the one-dimensional marginal distribution for the expected payoff E[g(S(t_n))] = E[S(t_n)].
a vector of length n with certificate prices
Stefan Wilhelm wilhelm@financial.com
Wilhelm, S. (2009). The Pricing of Derivatives when Underlying Paths Are Truncated: The Case of Express Certificates in Germany. Available at SSRN: http://ssrn.com/abstract=1409322
MonteCarlo.ExpressCertificate.Classic
and
MonteCarlo.ExpressCertificate
for Monte Carlo evaluation with similar
payoff functions
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