ExpressCertificate.Classic: Analytical and numerical pricing of Classic Express...

In fExpressCertificates: Structured Products Valuation for ExpressCertificates/Autocallables

Description

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

Usage

ExpressCertificate.Classic(S, X, T, K, g = function(S_T) {S_T}, 
  r, r_d, sigma, ratio = 1)

Arguments

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 g(S_T)=S_T
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

Details

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)].

Value

a vector of length n with certificate prices

Author(s)

Stefan Wilhelm [e-mail]

References

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

See Also

MonteCarlo.ExpressCertificate.Classic and MonteCarlo.ExpressCertificate for Monte Carlo evaluation with similar payoff functions

Examples

ExpressCertificate.Classic(S=100, X=c(100), 
  T=c(1, 2), g = function(S) { S }, 
  K=142.5, r=0.01, r_d=0, sigma=0.3, ratio = 1)

ExpressCertificate.Classic(S=100, X=c(100), 
  T=c(1, 2), g = function(S) { max(S, 151) }, 
  K=142.5, r=0.01, r_d=0, sigma=0.3, ratio = 1)    

fExpressCertificates documentation built on May 2, 2019, 11:02 a.m.