April 2015
Intermediate to advanced
1064 pages
33h 41m
English
book
Handbook of Multi-Commodity Markets and Products: Structuring, Trading and Risk Management
by Mark Cummins, Gianluca Fusai, Andrea Roncoroni
Content preview from Handbook of Multi-Commodity Markets and Products: Structuring, Trading and Risk Management
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APPENDIX A Quick Review of Distributions Relevant in Finance with Matlab® Examples*
Laura Ballotta and Gianluca Fusai
In this Appendix, we quickly review the properties of distributions relevant in finance, like the
- normal distribution
- lognormal distribution
- chi-square distribution
- non-central chi-square distribution
- Poisson distribution
- exponential distribution
- Gamma distribution
- multivariate Gaussian distribution.
We also present a standard procedure to simulate random variables via the so-called inverse method.
A.1 THE NORMAL DISTRIBUTION
Fact A.1.1 (Normal Distribution) A normal (Gaussian) random variable on ℜ with expected value μ ∈ ℜ and standard deviation σ ∈ ℜ+ has density function (pdf) ϕμ, σ(x) and cumulative distribution (cdf) Φμ, σ(x) given by:
and
We write 
. If μ = 0 and σ = 1 we have the so-called unit standard Gaussian random variable. In particular, if 
, then
Given the cdf, we can compute the probability that X falls in a given interval:
We produce
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I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.