Embedded Options, OAS & Structured Products

Learning objectives

By the end you can:

1. Decompose an option-embedded bond (callable = straight bond − call option, putable = straight bond + put option) and state who owns each option, when they exercise, and what that does to value.
2. Calibrate a binomial interest-rate tree to a benchmark par curve at a given volatility, and prove it arbitrage-free: every calibrating par bond reprices at exactly 100, and a straight bond prices identically on the tree and off the spot curve.
3. Value a callable and a putable node by node by backward induction, applying the exercise test at every decision node, and read off which nodes exercise and why.
4. Compute and distinguish nominal spread, Z-spread and OAS; compute option cost = Z-spread − OAS; and sign it correctly for a callable versus a putable.
5. Compute effective duration and effective convexity by curve-shift revaluation, say why modified duration and analytical convexity are invalid here, and demonstrate negative convexity numerically with a price ladder and an up/down capture ratio.
6. Handle mortgage prepayment: convert between CPR, SMM and PSA; build a pass-through cash flow month by month; compute WAL across speeds; and isolate the prepayment option as the sole cause of negative convexity by freezing the speed.
7. Tranche a pool and run its waterfall: a sequential-pay CMO whose principal ties to the collateral to the dollar, and an Indian PTC with over-collateralisation, subordination, cash collateral, excess spread and a loss trigger, then stress it and allocate the losses correctly.
8. Price a CDS from hazard rates: survival probabilities, the risky annuity (RPV01), the protection leg, the par spread; convert to an upfront at a standard coupon; invert a market spread to an implied hazard rate; bootstrap a two-point credit curve; and mark a position to market.
9. Situate all of it in both jurisdictions (R6): US agency/corporate callables, agency MBS and CMOs, standardised CDS, and India's putable/callable corporate bonds, the RBI Securitisation of Standard Assets framework (PTC/DA, MRR, MHP), and the thin single-name protection market that forces hazard rates to be inferred from bond spreads.
10. (Productivity objective: R10 duality.) Use AI and code to accelerate tree-building, waterfall modelling and curve bootstrapping, while running the verification that makes the output admissible: the tree reprices the curve, the waterfall sums, the credit curve reprices its own quotes.

The duality, stated once (R10). The understanding objective (items 1–9) is what the gate rewards; you earn the crown by building the tree, rolling the bond back and tying the waterfall by hand. The productivity objective (item 10) is the payoff you keep. But the duality is sharper here than anywhere else in the program, because the outputs are unfalsifiable by eye: an OAS of 56 bp and an OAS of 22 bp look equally reasonable on a page, and only the model that produced them tells you which is right. Verification here is not diligence; it is the entire skill.

Prerequisites & connections

Builds on. This is the crown of the FI branch and it assumes the branch. FI1.01 gave you pricing off a discount curve and the yield family (YTM, BEY, YTC, yield-to-worst), used here, and shown exactly where it breaks. FI1.02 gave you Macaulay/modified duration, PVBP/DV01 and analytical convexity, replaced here by effective (shift-and-revalue) versions, with the reason. FI1.03 gave you bootstrapping, spot and forward rates, and the arbitrage-free logic that a curve must reprice its own instruments, the tree calibration here is that discipline in two dimensions. From the analyst core: M1.08 for effective-interest amortization; M7.03 for what curve level and shape signal; E11.01 for the credit half, ratings, covenants, recovery, and the spread ≈ PD × LGD slide rule that the CDS section makes exact rather than approximate; M5.02 for how an Indian NBFC/HFC funds itself, the demand side of the securitisation market you will tranche. From the derivatives galaxy, DV1.02 owns option pricing proper (parity, risk-neutral valuation, BSM, the Greeks), this node uses risk-neutral backward induction as a tool and does not re-derive it.