Convertible Bond Arbitrage Data Requirements

When to Use

Use this skill when defining the data contract for a Convertible Bond (CB) arbitrage strategy, or when computing the screening metrics that sit on top of it: parity, conversion premium, bond floor, delta hedge size, and net carry. CB arbitrage buys a convertible (a hybrid of straight debt plus an equity conversion option) and shorts the underlying equity to isolate cheap implied volatility, carry, or credit mispricing while holding the package delta-neutral.

When NOT to Use

• As a convertible pricing model. Delta and implied volatility are inputs here. Producing them requires a CB model (binomial / Tsiveriotis-Fernandes style) that handles credit-risky conversion, issuer calls, puts and soft-call triggers. This module deliberately does not implement one.
• For busted (credit-like) converts. When parity sits far below the bond floor, the position is a credit trade, not a volatility trade; the screening logic flags this case and refuses to call it attractive.
• For live order routing. The short leg has its own regulatory and borrow-side obligations that this module does not enforce — see Related Skills.

Prerequisites

• Bond static terms: par value, conversion ratio (per the same nominal as par value), coupon rate, coupon frequency, maturity date.
• CB market data: clean price (points of par) and accrued interest.
• Equity market data: spot price, borrow fee, expected dividend yield.
• Credit data: issuer credit spread in basis points (required for the bond floor).
• Model/vendor analytics: equity delta and implied volatility.
• Funding terms: repo financing rate for the long CB leg, and the rate and haircut your prime broker applies to short-sale proceeds.
• Python 3.10+ (standard library only).

Workflow

1. Audit data completeness before computing anything. audit_data_completeness() separates missing inputs from present but invalid ones (NaN, infinite, negative, delta outside [0, 1]). evaluate_arbitrage() raises on a failed audit rather than screening on partial data — a single NaN price would otherwise propagate into every metric and surface as a silent "not attractive".
2. Compute parity and conversion premium, and state the basis. Parity = conversion ratio x stock price. Conversion premium % = (CB price - parity) / parity x 100. The CB price may be the quoted clean price (market convention, the default) or the full price including accrued interest. The two differ by up to a full coupon period, so a premium reported without its basis is not comparable across sources; configure it explicitly with premium_basis.
3. Size the short equity leg — check the delta convention first. Short shares = CB quantity x conversion ratio x delta, where delta is the per-share delta in [0, 1]. Desks and vendors also quote CB delta as shares per bond in [0, conversion_ratio]; passing that value into the same formula over-hedges by a factor of the conversion ratio. The [0, 1] bound is enforced to catch it. Round to the venue's lot size and carry the rounding residual as known open exposure.
4. Compute the bond floor from the issuer credit spread. The floor is the PV of the straight-bond cash flows discounted at risk-free + credit spread. It is the downside protection the trade is being paid for; it moves with the spread, so it must be recomputed on spread updates, not treated as a constant. If parity has fallen far below the floor, the convert is busted and equity-vol screening no longer applies.
5. Compute carry over the whole package, not the bond alone. `Net carry = coupon + interest on short proceeds - repo financing - stock borrow fee
   • dividends payable in lieu on the short. The last three hedge-leg terms scale with the **short position market value** (delta x parity`), not with bond notional — applying a borrow rate directly to bond notional misstates the drag whenever delta or the parity/price ratio is away from 1.
6. Screen, then decide. Cheap vol (HV - IV above threshold), a tolerable premium and acceptable carry make a candidate, not a trade. All thresholds are configurable (ScreenThresholds) and their defaults are desk heuristics with no authoritative basis — calibrate them against your own book before trading on them.

Full procedure: see references/workflows.md. Standards reference: see references/standards.md. Printable pre-flight checklist: see assets/checklist.md.

Common Pitfalls

• Charging the borrow fee against bond notional. The stock loan fee and the dividends owed in lieu are charged on the short equity market value (delta x parity). At delta 0.60 with parity 900 against a 1,000 bond, that base is 540, not 1,000 — a fee applied to bond notional overstates the drag by ~85% here, and the sign of net carry can flip.
• Forgetting dividends on the short leg. A short seller owes the lender substitute payments equal to any dividends paid. On a dividend-paying underlying this is often larger than the borrow fee and turns a positive-carry screen negative.
• Ignoring the stock borrow fee entirely. A hard-to-borrow underlying at a 15% fee wipes out coupon carry and volatility edge outright; borrow recall additionally forces an unplanned unwind of the hedge at the worst moment.
• Mixing up the two delta conventions. See workflow step 3 — the failure mode is a short position sized conversion_ratio times too large, which is a directional bet, not a hedge.
• Comparing conversion premiums computed on different price bases. Clean-basis and full-basis premiums are not the same number; vendor screens do not always say which they use.
• Static delta hedging. The package is long gamma: delta moves with spot, so an un-rebalanced hedge silently accumulates directional equity risk.
• Treating the convertible as risk-free debt. The bond floor is only a floor while the issuer performs. Spread widening lowers the floor and hits the long CB leg at the same time the equity leg is usually gaining least — the 2005 GM episode is the standard example of both legs losing together.

Verification

• ConvertibleBondArbitrageEngine().calculate_parity(20.0, 45.0) must return 900.0 (par 1,000, conversion ratio 20, spot 45).
• With a CB clean price of 99.0 (990 per bond), the clean-basis conversion premium must be 10.0% — independently: market conversion price 990 / 20 = 49.50, premium per share 4.50, ratio 4.50 / 45.00 = 10%.
• calculate_delta_hedge_quantity(100, 20.0, 0.60) must return 1200 shares, and passing 12.0 (the shares-per-bond form of the same delta) must raise ValueError.
• With par 1,000, a 4% annual coupon paid semi-annually, 3 years to maturity, a 4% risk-free rate and a 300bp credit spread, the bond floor must equal the closed-form annuity value 20 x (1 - 1.035^-6)/0.035 + 1000 x 1.035^-6 = 920.07.
• With accrued 10 (full price 1,000), parity 900, delta 0.60, borrow 1%, dividend yield 2%, repo 4.5% and 4% on short proceeds, net carry must be 40 + 21.6 - 45 - 5.4 - 10.8 = +0.40 per bond (+4bp on the full price).
• Run python -m unittest discover -s skills/convertible-bond-arbitrage-data-requirements/scripts.

Related Skills

• options-implied-volatility-surface-construction
• cross-asset-hedge-execution-synchronization
• short-selling-borrow-cost-and-availability-modeling
• us-reg-sho-short-sale-locate-requirements
• counterparty-credit-risk-for-otc-derivatives