convertible-bond-arbitrage-data-requirements v1.1.0A

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---
name: convertible-bond-arbitrage-data-requirements
description: Quantitative fixed-income and equity derivatives module for auditing Convertible
  Bond (CB) Arbitrage data completeness and computing parity, conversion premium, bond
  floor from the issuer credit spread, delta hedge sizing, and the full carry breakdown
  of a delta-hedged CB package.
domain: Derivatives & Fixed Income
subdomain: Convertible Securities
tags:
- convertible-bond
- arbitrage
- delta-hedging
- parity
- conversion-premium
- credit-spread
- borrow-rate
brokers_frameworks:
- Python Standard Library
- Generic Fixed Income
version: "1.1.0"
author: algo-trading-skills-contributors
license: Apache-2.0
---

## 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 3.9+ (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`