fExpressCertificates (version 1.3)

SimulateExpressCertificate: Monte Carlo Valuation of Express Certificates

Description

Generic Monte Carlo Valuation of Express Certificates using the Euler scheme, multivariate normal distribution and truncated multivariate normal.

Usage

SimulateGenericExpressCertificate(S, X, K, T, r, r_d, sigma, mc.loops = 10000, 
  mc.steps = 1000, payoffFunction = payoffExpressClassic, ...)
SimulateExpressClassicCertificate(S, X, K, T, r, r_d, sigma, mc.loops = 10000, 
  mc.steps = 1000)
SimulateExpressBonusCertificate(S, X, B, K, T, r, r_d, sigma, mc.loops = 10000, 
  mc.steps = 1000, barrierHit = FALSE)
  
simExpressPriceMVN(S, m = Inf, X, K, B, T, r, r_d, sigma, 
  mc.loops = 100000, payoffFunction, ...)
simExpressPriceTMVN(S, m = Inf, X, K, B, T, r, r_d, sigma, 
  mc.loops = 100000, payoffFunction, ...)

Arguments

S

the asset price, a numeric value

X

a vector of early exercise prices/call levels ("Bewertungsgrenzen"), vector of length (n-1)

B

barrier level

K

vector of fixed early cash rebates in case of early exercise, length (n-1) or n in case of a fixed rebate at maturity

T

a vector of evaluation times measured in years ("Bewertungstage"), vector of length n

r

the annualized rate of interest, a numeric value; e.g. 0.05 means 5% 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.

mc.loops

Monte Carlo Loops (iterations)

mc.steps

Monte Carlo steps in one path

barrierHit

flag whether the barrier has already been reached/hit during the lifetime

payoffFunction

definition of a payoff function, see details below

m

The minimum price up to today for pricing during the lifetime.

…

Additional parameters passed to the payoff function

Value

The methods return an object of class "express.certificate".

An object of class "express.certificate" is a list containing at least the following components:

price

Monte Carlo estimate

prices

A vector of simulated discounted prices (length mc.loops)

n

The number of valuation dates

redemptionTimes

A vector of redemption times i = 1..n (length mc.loops)

S

the asset price, a numeric value

X

early exercise prices/call levels

K

vector of fixed early cash rebates in case of early exercise

T

a vector of evaluation times measured in years ("Bewertungstage")

There is also a method print.express.certificate for pretty printing of express.certificate objects.

Details

TO BE DONE: Definition of payoff functions

See Also

Definition of several payoff functions in payoffExpressClassic, payoffExpressCappedBonusType1 or payoffExpressBonusType1

print.express.certificate for pretty printing of express.certificate objects

Examples

# NOT RUN {
# Example CB7AXR on Deutsche Telekom on 10.12.2009
p <- SimulateExpressBonusCertificate(S=10.4/12.10*100, X=c(100,100,100), B=7/12.1*100, 
    K=c(134, 142.5, 151), 
	T=.RLZ(c("16.12.2009","17.06.2010","17.12.2010"), start="10.12.2009"), r=0.01, r_d=0, 
	sigma=0.23, mc.loops=10000, mc.steps=1000)
p
# }