- 292 pages
- English
- PDF
- Available on iOS & Android
eBook - PDF
Monte Carlo Simulation with Applications to Finance
About this book
Developed from the author's course on Monte Carlo simulation at Brown University, this text provides a self-contained introduction to Monte Carlo methods in financial engineering. It covers common variance reduction techniques, the cross-entropy method, and the simulation of diffusion process models. Requiring minimal background in mathematics and finance, the book includes numerous examples of option pricing, risk analysis, and sensitivity analysis as well as many hand-and-paper and MATLAB coding exercises at the end of every chapter.
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Yes, you can access Monte Carlo Simulation with Applications to Finance by Hui Wang in PDF and/or ePUB format, as well as other popular books in Business & Finance. We have over one million books available in our catalogue for you to explore.
Information
Chapter
1
Review
of
Probability
Probability
theory
is
the
essential
mathematical
tool
for
the
design
and
analysis
of
Monte
Carlo
simulation
schemes.
It
is
assumed
that
the
reader
is
somewhat
familiar
with
the
elementary
probability
concepts
such
as
ran-
dom
variables
and
multivariate
probability
distributions.
However,
for
the
sake
of
completeness,
we
use
this
chapter
to
collect
a
number
of
basic
re-
sults
from
probability
theory
that
will
be
used
repeatedly
in
the
rest
of
the
book.
1.1
Probability
Space
In
probability
theory,
sample
space
is
the
collection
of
all
possible
outcomes.
Throughout
the
book,
the
sample
space
will
be
denoted
by
Ω
.
A
generic
element
of
the
sample
space
represents
a
possible
outcome
and
is
called
a
sample
point
.
A
subset
of
the
sample
space
is
called
an
event
.
1.
The
empty
set
is
denoted
by
∅
.
2.
The
complement
of
an
event
A
is
denoted
by
A
c
.
3.
The
intersection
of
events
A
and
B
is
denoted
by
A
∩
B
or
simply
AB
.
4.
The
union
of
events
A
and
B
is
denoted
by
A
∪
B
.
A
probability
measure
P
on
Ω
is
a
mapping
from
the
events
of
Ω
to
the
real
line
R
that
satisfies
the
following
three
axioms:
(i)
P
(
Ω
)
=
1.
Table of contents
- Front Cover
- Preface
- Contents
- 1. Review of Probability
- 2. Brownian Motion
- 3. Arbitrage Free Pricing
- 4. Monte Carlo Simulation
- 5. Generating Random Variables
- 6. Variance Reduction Techniques
- 7. Importance Sampling
- 8. Stochastic Calculus
- 9. Simulation of Diffusions
- 10. Sensitivity Analysis
- A. Multivariate Normal Distributions
- B. American Option Pricing
- C. Option Pricing Formulas
- Bibliography