Financial Derivatives/Notions of Probability Theory

Notions of Probability Theory

Here we introduce the notions of probability theory essential for the understanding of the book. The interested reader is referred to more thorough accounts of probability theory.

Useful distributions

Discrete distributions

For a thourough list of discrete distributions and their properties the interested reader is referred to Wikipedia on discrete distributions.

Binomial Distribution

The binomial distribution of parameters $n\in {\mathcal {N}}$ and $p\in [0,1]$

$P(X=k)={n \choose k}p^{k}(1-p)^{n-k}$

Poisson distribution

The poisson distribution with parameter $\lambda >0$, the intensity

$P(X=k)={\frac {\lambda ^{k}}{k!}}e^{-\lambda }$