CM2 Financial Engineering & Loss Reserving

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Learn CM2 free — 24 worked explainers

One idea per page, explained from scratch, each ending in a worked example with the arithmetic shown in full. These are the ideas students most often get stuck on in CM2. Start anywhere.

1. 01 Utility theory and risk aversion: non-satiation, A(w) and R(w) Test a utility function for non-satiation and risk aversion, and calculate the largest premium a person would pay to remove a risk Read
2. 02 Measures of investment risk: variance, semi-variance, VaR and Tail VaR Calculate variance, semi-variance, shortfall probability, Value at Risk and Tail Value at Risk, and say which measure suits which decision Read
3. 03 CAPM and the security market line: beta and the market price of risk Use the security market line to find an expected return, a beta or the market return, and check the result against the value-weighted market Read
4. 04 Ito's lemma explained term by term, and what it does to a share price Apply Ito's lemma to a function of a stochastic process and read the distribution of the result Read
5. 05 The chain ladder method: estimating outstanding claims from a run-off triangle Calculate development factors from a run-off triangle and project the outstanding claims reserve, checking the answer by a second route Read
6. 06 The Bornhuetter-Ferguson method: the chain ladder with a second opinion Calculate a Bornhuetter-Ferguson reserve and show it is a credibility weighting of the chain ladder and the premium-based estimate Read
7. 07 Binomial option pricing: where the risk-neutral probability comes from Price a European and an American option on a binomial tree, and explain why the real probability of a rise does not appear Read
8. 08 The Black-Scholes formula and put-call parity, read term by term Price a European call and put with the Black-Scholes formula, verify the put by put-call parity, and calculate delta and gamma Read
9. 09 Ruin theory: the adjustment coefficient and Lundberg bound explained Calculate the adjustment coefficient for a compound Poisson surplus process, bound the probability of ruin, and say what reinsurance does to both Read
10. 10 Mean-variance portfolio theory: the efficient frontier and why diversification works Calculate the mean and variance of a portfolio, find the minimum-variance combination of two assets, and explain the effect of correlation on the frontier Read
11. 11 The term structure: spot rates, forward rates and par yields Convert between spot rates, forward rates and par yields, and explain what each one is used for Read
12. 12 Short-rate models: Vasicek, Cox-Ingersoll-Ross and Hull-White compared Read the Vasicek, Cox-Ingersoll-Ross and Hull-White equations term by term, calculate the mean and variance of the Vasicek short rate, and state what each model fixes Read
13. 13 The Merton model: company equity as an option, and where a credit spread comes from Value a company equity and debt with the Merton model, find the risk-neutral default probability and the credit spread, and state the limitations Read
14. 14 The Greeks: delta, gamma, vega, theta and rho, and how a hedge decays Calculate the five Greeks for a European option, construct a delta hedge, and explain why gamma determines what the hedge costs to maintain Read
15. 15 The inflation-adjusted chain ladder: taking past inflation out and putting a future assumption in Restate a run-off triangle into current money, develop it, and inflate the projected payments forward at an explicit future assumption Read
16. 16 The average cost per claim method: developing numbers and severity separately Project a reserve by developing claim numbers and average cost per claim separately, and interpret what the split reveals Read
17. 17 Valuing a maturity guarantee by simulation, and checking it against the formula Value a maturity guarantee by Monte Carlo simulation, state its standard error, and explain why the simulation must run under the risk-neutral measure Read
18. 18 The Efficient Markets Hypothesis: the three forms, and how each one is tested State the three forms of the Efficient Markets Hypothesis, decide which form a piece of evidence bears on, and test for a pattern against its standard error Read
19. 19 Single-index and multifactor models: getting a covariance matrix out of a few betas Use a factor model to find an asset variance, a covariance between two assets and a portfolio variance, and name the three types of multifactor model Read
20. 20 Excess-of-loss reinsurance: the retained claim, and choosing the retention Find the mean and moment generating function of a claim retained under excess of loss, and locate the retention that maximises the adjustment coefficient Read
21. 21 State price deflators: pricing with real-world probabilities Construct state price deflators for a one-period binomial market, price assets with them, and explain how they produce a risk premium Read
22. 22 What makes a risk insurable, and what to do when it almost is State the conditions for a risk to be insurable, identify which condition a given risk fails, and quantify what a deductible does to the cost of a risk Read
23. 23 Two-state and intensity credit models: backing a default rate out of a bond price Imply a default intensity from a corporate bond price, calculate the credit spread exactly and by approximation, and compare the three families of credit model Read
24. 24 The martingale representation theorem, and why hedging is possible at all Verify that a discounted price is a martingale under the risk-neutral measure and identify the representation integrand as the hedging strategy Read

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