Credit risk

Part 1 gave events and expectations over a partition, present value, and risk-neutral pricing weights. This part applies them to a new event, the default of a reference entity. Default and survival partition the outcomes at each future date, so a survival curve gives default probabilities, and a risky payment is valued as a discounted expectation over the survival and default states.

This part introduces the default time of a reference entity in the course’s toy models. The first chapter reads an input survival curve, calculates the default probability of each interval, and uses a constant hazard rate. The second chapter values one claim under recovery of par: it pays its full amount on survival and a recovered fraction of par on default, both at maturity, and the claim’s value is the discounted expectation of those two payments.

Part 6 of 72 chapters1 numbered equations2 knowledge checks

1. Default, hazard, and survival

   Read an input survival curve, calculate interval default probabilities, and use a constant-hazard toy model.

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2. Recovery and one-period risky present value

   Value a narrowly defined recovery-of-par claim whose survival and default-state payments both occur at maturity.

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The argument

1. The default time is random, and survival to a date is an event
2. A survival curve gives the default probability of each interval
3. A constant hazard rate gives an exponential survival curve
4. Recovery of par sets the payment in the default state
5. A risky payment is the discounted expectation over survival and default

After this part you can

• Interpret survival probability as the modeled probability, conditional on survival at valuation time, of no default through a stated future time.
• Calculate time-zero cumulative or interval default probability from survival probabilities at stated times.
• Interpret a hazard rate as an instantaneous conditional default intensity, measured per unit of time, among names that have survived to that time.
• Calculate survival probability as S(0,t) = exp(-lambda t) under a stated non-negative constant hazard rate and consistent time units.
• Interpret the recovery rate as the fraction of par paid at maturity after default in the lesson's one-period recovery-of-par model.
• Calculate loss given default as one minus the recovery rate in the lesson's fractional recovery-of-par model.
• Calculate the time-zero present value of a one-period recovery-of-par claim by probability-weighting its survival and default payoffs at maturity and applying the stated discount factor.

Builds on

• Foundations

Leads to

• Bond options
• CDS