MonteCarlo.ExpressCertificate.Classic: Monte Carlo valuation of Classic Express Certificates

In fExpressCertificates: Structured Products Valuation for ExpressCertificates/Autocallables

Description

Monte Carlo valuation methods for Express Classic Certificates using the Euler scheme or sampling from conditional densities

Usage

MonteCarlo.ExpressCertificate.Classic(S, X, T, K, r, r_d, 
  sigma, ratio = 1, mc.steps = 1000, mc.loops = 20)
Conditional.MonteCarlo.ExpressCertificate.Classic(S, X, T, K, r, r_d, 
  sigma, ratio = 1, mc.loops = 20, conditional.random.generator = "rnorm")
MonteCarlo.ExpressCertificate(S, X, T, K, B,  
 r, r_d, sigma, mc.steps = 1000, mc.loops = 20, payoff.function)  

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)
B	barrier level
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
mc.steps	Monte Carlo steps in one path
mc.loops	Monte Carlo Loops (iterations)
conditional.random.generator	A pseudo-random or quasi-random (Halton-Sequence, Sobol-Sequence) generator for the conditional distributions, one of "rnorm","rnorm.halton","rnorm.sobol"
payoff.function	payoff function

Details

The conventional Monte Carlo uses the Euler scheme with mc.steps steps in order to approximate the continuous-time stochastic process.

The conditional Monte Carlo samples from conditional densities f(x_{i+1}|x_i) for i=0,…,(n-1)), which are univariate normal distributions for the log returns of the Geometric Brownian Motion and Jump-diffusion model: f(x_1,x_2,..,x_n) = f(x_n|x_{n-1}) \cdot … \cdots f(x_2|x_1) \cdot f(x_1|x_0) The conditional Monte Carlo does not need the mc.steps points in between and has a much better performance.

Value

returns a list of

stops	stops
prices	vector of prices, length mc.loops
p	Monte Carlo estimate of the price = mean(prices)
S_T	vector of underlying prices at maturity

Author(s)

Stefan Wilhelm [e-mail]

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