Clean and Dirty Prices as Underlyings for Bond Options

Summary

The document explains the distinction between clean (quoted) and dirty (cash) bond prices when specifying a bond option. Its answer emphasizes that over-the-counter contracts can define their strike and underlying price according to the parties’ chosen conventions. In common arrangements, the strike uses the same clean or dirty convention as the bond quotation, though the two conventions can also be mixed by agreement. Yield or asset-swap spread strikes are mentioned as less frequent alternatives.

Dirty bond prices accumulate accrued interest between coupons and drop when a bond goes ex-coupon, creating a sawtooth pattern. That predictable accrual does not prevent parties from writing an option on either price convention. The discussion describes market convention and contract flexibility, but gives no option-pricing derivation or empirical comparison of clean-price and dirty-price models. The cited Black–Scholes modeling concern is therefore not resolved mathematically in the material.

Key ideas

• Bond option contracts can specify either clean or dirty bond prices as the underlying convention.
• The strike convention commonly matches the bond quotation, but parties can agree to other combinations.
• Dirty prices rise with accrued interest and fall when a coupon goes ex-coupon.
• Yield and asset-swap spread strikes are noted as less common alternatives.
• The document does not derive how the chosen price convention affects an option-pricing model.

Tags

# Bond Option: Cash Price or Quoted Price as Underlying


# Bond Option: Cash Price or Quoted Price as Underlying












John Hull mentioned in his book using Cash Price(Dirty Price) instead of Quoted Price(Clean Price) in pricing a bond option using Black-Scholes. It confuses me as it seems more natural to assume the return of bond price stripped off accrued interest follows a Geometric Brownian Motion. Accrued interest itself does not have any stochastic components.

Does anybody have a good explanation on this distinction?

## Answer by Dimitri Vulis (score 1)

https://quant.stackexchange.com/a/74064

Bond options are traded over the counter. Whatever the parties want to agree to, they can write down on their term sheet. Bond options are also not very common these days, but I've seen a few.

The strike is almost always a price of the bond. Usually, if the bond is quoted clean (without accrued, usually the case in developed markets), then the strike is also a clean price. Conversely, if the bond is quoted dirty (on proceeds, with acctrued), then the strike is also a dirty price. Much less often, the strike is a yield or an asset swap spread.

The dirty price of a (performing) bond looks like a saw: it grows every day, then drops when a coupon goes ex. Nothing stops the parties, e.g. from trading an option, whose strike is a clean price, even though the market convention of the underlying bond is a dirty price, or vice versa, if they prefer.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.