Explain expected exposure, probability of default, loss given default and the adjustment to value for credit (CVA)

Credit risk splits into four pieces. Expected exposure is the amount at stake if default occurred at a given date, before any recovery, usually the value of the remaining payments at that date. Loss given default is exposure × (1 − recovery rate). The probability of default for a period is the hazard rate multiplied by the probability of surviving to the start of that period, so it falls over time even with a constant hazard. Expected loss for a date is loss given default × probability of default. The credit valuation adjustment is the sum of each expected loss discounted at the risk-free rate, and a bond's fair value is its default-free value minus the CVA.