Nonparametric Finance

Chapter 8Quantiles and Value-at-Risk

In quantile estimation, we study such questions as:

1. 1. How much liquid capital a bank must possess in order that the probability of running out of cash during the next month is smaller than 1/10,000?
2. 2. How much cash must be deposited in a margin account in order that the probability that cash does not cover the losses of a futures position during the next day is smaller than 1/10,000?

These questions can be formulated using the concepts of probability theory. Let be a real valued random variable. Let be a probability. The th quantile is the smallest number so that . In the first example random variable is the monthly loss of the investment portfolio of a bank. In the second example random variable is the daily loss of a futures position.

We want ...