Measuring interest rate and credit risk
Investment risks from holding bonds
Other risks associated with bonds
Duration
Properties of duration
Immunisation (1)
Immunisation (2)
Convexity
Credit spread
Credit yield curves
Risk neutral probabilities of default (1)
Risk neutral probabilities of default (2)
Historical probabilities of default
See you in the next lecture

Risk neutral probabilities of default (1)
Expected value
Expected value = Σn (probability of n-th outcome) × (value of n-th outcome)
Objective certainty: The law of large numbers ensures that the expected value is a sure event to take place if the risky game is repeated many times
Subjective certainty: The expected value of a one-off experiment is subjectively regarded as a sure event that will happen

Risk-neutral environment
Application of no-arbitrage condition to the risky environment: today’s price of the two investments, identical in the size of return and risk, must be the same

Investments earning just the expected value (sure outcome)should generate risk-free returns
The expected value of the investment when discounted at a risk-free rate of return should be equal to the current value of the investment

Risk neutral probabilities are theoretical probabilities consistent with the risk-neutral environment (as opposed to empirical probabilities)