Structured Products
Everything here is decomposition: a structured product is a bundle of simpler claims, and the exam wants you to unbundle it, price the pieces, and say who is short which option.
Term structure modelling
Two families, and the distinction between them is the most reliably tested idea in this part.
Equilibrium models
Specify a process for the short rate from economic assumptions and derive the whole curve. Vasicek: dr = κ(θ − r)dt + σ dz — mean reversion to θ at speed κ with constant volatility, closed-form bond prices, but rates can go negative. Cox–Ingersoll–Ross: volatility scaled by √r, so volatility falls as rates approach zero and rates stay non-negative.
Strength: economic interpretation and parsimony. Weakness: with a handful of parameters the model will not reprice every observed bond, so it cannot be used for arbitrage-free relative-value pricing of derivatives against the current curve. Both are single-factor, so all rates move together — they cannot generate independent curve twists.
Arbitrage-free (no-arbitrage) models
Take today's observed curve as given and fit the model to it exactly, then price derivatives consistently with it. Ho–Lee adds a time-dependent drift to a normal short rate; Hull–White is essentially Vasicek with a time-dependent drift so the initial curve is matched; Black–Derman–Toy works in a binomial lattice on the log of the rate, keeping rates positive and calibrating to both the curve and volatilities.
Strength: exact consistency with market prices, which is a requirement for pricing and hedging interest-rate options. Weakness: calibrated parameters have no economic content, they must be re-fitted continually, and a model that fits today perfectly may imply implausible future dynamics.
How to choose in an answer: equilibrium models for economic scenario generation, long-horizon asset-liability projection and understanding drivers; arbitrage-free models for pricing and hedging traded derivatives against the current curve. Saying which purpose the model serves is what earns the mark.
Interest rate derivatives
The consistent exam move is to convert a structure into the bond-plus-options equivalent and then ask about convexity and negative convexity. A callable bond's upside is capped because the issuer calls when rates fall — negative convexity — which is why its price appreciation lags a comparable non-callable bond in a rally and why its yield is higher.
Asset-backed securities
The structure. Assets are sold to a bankruptcy-remote special purpose vehicle, which issues tranches of differing seniority. Credit enhancement comes from subordination, overcollateralisation, excess spread, and reserve accounts; the resulting waterfall pays interest and principal by seniority. The economic point is tranching: the same pool of assets is divided into claims with very different risk — a senior tranche is protected by everything below it, an equity or residual tranche absorbs first losses and is highly leveraged to the pool's loss rate.
Correlation is the hidden variable. For a given expected pool loss, higher default correlation makes extreme outcomes more likely, which harms senior tranches (they can now be reached) and can help equity tranches (a chance of very few defaults). Investors in a senior tranche are therefore implicitly short correlation — the lesson learned expensively in 2007–08, and a favourite examinable subtlety.
Prepayment and extension risk generalise: faster prepayment shortens the life and returns cash when reinvestment rates are low; slower prepayment extends it. That is why average life, not stated maturity, is the relevant horizon for any amortising structure, and why an ABS investor's yield is model-dependent.
Insurance-linked securities: catastrophe bonds
The structure. A sponsor (an insurer or reinsurer) transfers catastrophe risk to capital markets through a special purpose vehicle that issues notes and holds the proceeds as collateral. Investors earn a spread over the collateral yield; if a defined event triggers the bond, principal is reduced to pay the sponsor's losses. The attachment point is the loss level at which investors begin to lose principal and the exhaustion point is where they lose all of it; the modelled probability of reaching attachment is the basis for pricing, expressed as a multiple of expected loss.
Four trigger types — the most examinable list in the chapter, because each shifts basis risk and moral hazard between the parties:
Investment characteristics. The risk driver is meteorological or seismic, so correlation with financial assets is genuinely low and remains low through financial crises — the core diversification case. Against that: negatively skewed returns with severe tail losses, catastrophe-model risk (and non-stationarity as climate changes), loss creep and delayed settlement on indemnity structures, trapped collateral, seasonality of peril exposure, and concentration of the market in a few perils and regions.
Life ILS: longevity & mortality risk
Two opposite exposures. Mortality risk is the risk that people die sooner than expected — the exposure of a life insurer, hedged with mortality catastrophe bonds that trigger on a spike in a population mortality index (pandemic, war, natural disaster). Longevity risk is the risk that people live longer than expected — the exposure of an annuity provider or a defined benefit pension plan, hedged with longevity swaps, longevity bonds and reinsurance.
Longevity swaps are the practically important instrument: the pension plan pays a fixed schedule of payments and receives payments matching the actual experience of its members, converting an uncertain lifetime liability into a fixed one. Structures are either indemnity/bespoke — matched to the plan's own members, no basis risk, expensive and slow to execute — or index-based, referencing a national population index, cheaper and faster but leaving the plan with basis risk between its members' longevity and the index. A pension question that mentions "hedging longevity" is asking you to make exactly this trade-off.
Life settlements complete the set: purchasing an in-force life insurance policy from the insured at more than surrender value but less than face value, then paying the premiums and collecting the death benefit. The return depends on life-expectancy estimation, so the risk is that the insured lives longer than underwritten (extension risk) plus premium-cost escalation, and the market carries genuine ethical and reputational considerations that an institutional investor must address explicitly.
Why these appeal to institutions: the driver is demographic rather than financial, giving low correlation to markets. Why they are hard: pricing depends on actuarial models with long horizons and structural trend uncertainty (medical advances), liquidity is minimal, valuation is model-based, and counterparty exposure on a decades-long swap is material — which is why collateralisation terms are a central negotiating point.
Hybrid products: mezzanine debt
Where it sits. Mezzanine is subordinated debt ranking between senior secured debt and equity, used chiefly in buyouts and mid-market growth financing when senior lenders will not stretch far enough and the sponsor does not want to issue more equity. It is a hybrid because its return is engineered from several components: a cash coupon, often a PIK (payment-in-kind) accrual, arrangement and exit fees, and an equity kicker in the form of warrants or a conversion right.
Why it exists. For the borrower it is cheaper than equity and less dilutive, typically with looser covenants, bullet maturity and no amortisation; for the sponsor it increases the leverage available and therefore equity returns. For the lender it offers an equity-like return with a contractual claim ahead of equity — the classic risk-return middle ground.
In an allocation answer: mezzanine and private credit generally are hired for contractual income with equity-like return, funded from either the credit or the return-seeking sleeve depending on the institution's framing — and the honest caveat is that in a severe downturn its correlation with private equity is high, because it is exposure to the same companies further down the same capital structure.
Confusion pairs
Practice
Six multiple-choice questions in exam style, with the reasoning — not just the letter.
1. An analyst must price a portfolio of swaptions consistently with today's observed yield curve. The most appropriate model family is:
2. Holding expected pool loss constant, an increase in default correlation across an ABS collateral pool most likely:
3. A sponsor wants a catastrophe bond with no basis risk to its own losses. The appropriate trigger, and its consequence for investors, is:
4. A defined benefit plan enters an index-based longevity swap rather than a bespoke one. The principal consequence is:
5. Which feature of mezzanine debt most increases risk as a borrower deteriorates?
6. Credit card ABS differ structurally from auto loan ABS principally because:
Constructed-response practice
Write these under time. Each outline is the shape the rubric rewards, not a model answer to memorise.
Prompt A (14 minutes). A pension plan is considering a 3% allocation to catastrophe bonds. Explain the investment case, the four principal risks, and how you would implement and monitor the allocation.
- Case: a non-financial risk driver, so genuinely low correlation that persists in financial crises; spread over collateral yield; contractual, defined triggers.
- Risk 1 — negative skew and tail severity: many small gains, rare large principal losses.
- Risk 2 — model risk in the catastrophe model, aggravated by climate non-stationarity in the historical hazard record.
- Risk 3 — basis, settlement and structural risks by trigger type; loss creep and trapped collateral on indemnity structures.
- Risk 4 — concentration by peril, region and season, plus limited liquidity in the secondary market.
- Implementation: diversified fund or mandate across perils and regions rather than single bonds; sizing on stress loss, not volatility; monitoring modelled expected loss, attachment probabilities, exposure by peril and season, and independent review of the model vendor.
Prompt B (12 minutes). A mid-market buyout sponsor offers a mezzanine tranche at a 10% cash coupon plus 3% PIK plus warrants. Assess the risk-return proposition for an insurer, and identify the three documentation terms you would examine most closely.
- Decompose the return: cash coupon, PIK accrual, fees, and warrant value dependent on the exit — note that the last makes the return partly equity-like.
- Risk: subordination implies low recovery in default, so downside is closer to equity than to senior debt; PIK compounds exposure as stress builds.
- Insurer-specific lens: capital treatment and rating-agency view, valuation of an unquoted model-marked asset, and the correlation of the position with the plan's other private-equity exposure.
- Terms: the intercreditor agreement (payment blockage, standstill, enforcement rights), covenant package and equity-cure provisions, and the warrant/conversion mechanics including anti-dilution.
- Conclude with the condition for proceeding — for example only within a diversified private-credit mandate, sized on stress-case recovery rather than on the headline coupon.