Description Usage Arguments Details Value Author(s)
Monte Carlo valuation methods for Express Classic Certificates using the Euler scheme or sampling from conditional densities
1 2 3 4 5 6 | 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)
|
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 |
payoff.function |
payoff function |
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.
returns a list of
stops |
stops |
prices |
vector of prices, length |
p |
Monte Carlo estimate of the price = |
S_T |
vector of underlying prices at maturity |
Stefan Wilhelm wilhelm@financial.com
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