Pricing a Plain Bond with a Hull–White Tree Engine

Summary

The document addresses whether QuantLib’s Hull–White tree engine for callable fixed-rate bonds can value an otherwise plain bond, so the callable bond’s option value can be inferred by comparing the two prices. The answer says the engine cannot be used directly for that purpose through a plain bond instrument.

The proposed workaround is to create a callable bond with an empty callability schedule and price it with the same tree engine. Its value serves as the plain-bond value for comparison with the callable bond’s net present value. The response is a concise implementation suggestion; it provides no derivation, numerical example, or discussion of assumptions such as curve setup and model calibration, which remain relevant to accurate valuation.

Key ideas

• The callable-bond Hull–White tree engine does not directly price a plain bond in the described setup.
• A callable bond with an empty callability schedule can be used to obtain a plain-bond value from the same engine.
• Comparing that value with the callable bond value can help isolate the embedded call option value.
• The discussion gives no numerical validation or details about model and yield-curve assumptions.

Tags

# Pick the price of plain bond off Hull-White Tree


# Pick the price of plain bond off Hull-White Tree












Since we can use Hull-White tree to calculate the price of a option embedded bond, which can be achieved by the QuantLib pricing engine TreeCallableFixedRateBondEngine, can this engine be also used to calculate the plain bond price, therefore we can calculate the option price by deducting callable bond npv from plain bond npv?

## Answer by Luigi Ballabio (score 1)

https://quant.stackexchange.com/a/79687

Not directly. However, you can instantiate another callable bond with an empty callability schedule and use `TreeCallableFixedRateBondEngine`. This will give you the value of the plain bond.

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.