Default counts, return-loss probabilities and terminal-price scenarios need a probability distribution. This lesson connects probability masses, densities and cumulative probabilities to those calculations. It derives binomial moments from default indicators and a lognormal CDF from normal log returns. These are model calculations: the chosen distribution and independence assumptions must fit the risk being studied.
Learning objectives. By the end of this note you should be able to:
- define discrete and continuous random variables via PMF/PDF and recover probabilities from the CDF;
- compute and from a PMF or PDF, and use linearity of expectation without independence;
- state the Bernoulli, binomial, Poisson, normal, lognormal and exponential laws with their finance readings;
- derive and for from the Bernoulli indicator decomposition;
- obtain the CDF of a lognormal price from a normal log-return.
In this lesson
- Discrete and continuous random variables
- Expectation and variance
- Named discrete laws
- Named continuous laws
- Functions of a random variable
- Worked finance examples
Before you start
The full lesson, with worked examples and exercise solutions, is for members.
Read the full lessonNew to SelfMadeQuant.com? See membership options or browse the Probability, Statistics and Financial Data syllabus.