---
description: "Simultaneously buy and sell two convertible bonds from the same issuer, long the higher option-adjusted spread and short the lower, profiting when the spreads converge."
tags: [convertibles, arbitrage, fixed-income]
---

# Convertible Option-Adjusted Spread (OAS) Arbitrage

**Section**: 12.2 | **Asset Class**: Convertibles (Hybrid: Fixed Income + Equity) | **Type**: Relative Value / Arbitrage

## Overview
This strategy simultaneously buys and sells two different convertible bonds issued by the same company. The long position is in the bond with the higher option-adjusted spread (OAS) and the short position is in the bond with the lower OAS. The trade is profitable when the two spreads converge toward each other.

## Construction / Mechanics
The price of a convertible bond is decomposed as:

```
P_C = P_B + V                (494)
```

- `P_C` = convertible bond price
- `P_B` = straight bond price (the bond without the embedded option), computed via standard discounting of future cash flows
- `V` = value of the conversion option (a call option on the issuer's stock)

**OAS Calculation Procedure:**
1. At the initial iteration, compute `V^(0)` using a call option pricing model with the zero-coupon government Treasury curve as the risk-free rate
2. Check if `V^(0)` matches the market-implied option value `P_C^mkt - P_B`
3. If not, iteratively parallel-shift the Treasury curve (e.g., using bisection) until the computed `V` equals `P_C^mkt - P_B`
4. The parallel shift obtained is the OAS

## Return Profile
Profits when the OAS of the long bond decreases (price rises) and/or the OAS of the short bond increases (price falls), i.e., when the two spreads converge. Returns are driven by relative mispricing between the two convertibles of the same issuer, not by the absolute level of spreads or interest rates.

## Key Parameters / Signals
- **OAS differential**: the spread between the two bonds' OAS values; wider differential implies larger potential profit but also higher risk if divergence continues
- **Same-issuer requirement**: both bonds must be from the same issuer to neutralize credit risk
- **Convergence horizon**: the expected time for OAS convergence to occur

## Variations
- **Multi-bond basket**: extend to a basket of convertibles from the same issuer, weighting by OAS rank
- **Cross-issuer OAS**: relax the same-issuer constraint and use credit hedges to neutralize issuer-level credit risk

## Notes
- The OAS computation requires an option pricing model for `V`; model risk affects both legs
- The iterative parallel-shift procedure assumes the Treasury curve shape is fixed; actual curve shape changes can affect the OAS estimate
- Liquidity mismatch between the two convertible bonds can create mark-to-market losses even when the fundamental trade thesis is correct
- This strategy is distinct from straight convertible arbitrage (12.1): there is no stock short; both legs are bonds from the same issuer