Pricing American Options on Bond Futures with Delivery Optionality
Summary
The document sketches a layered approach to pricing an American option on a bond futures contract. First, use a term-structure model to simulate yields or prices for all deliverable bonds across relevant dates. Short-rate models such as Vasicek or Hull–White are examples; another suggested approach is to diffuse yields using a small number of principal components. Next, calculate the futures value on each tree node or simulated path by accounting for which bond is cheapest to deliver, then use that futures process to value the American option, for example through a lattice or Monte Carlo least-squares method.
The sketch simplifies the futures’ own delivery features: it proposes assuming delivery on the last delivery date while ignoring end-of-month and timing options. It gives no calibration results or worked example, and stresses that delivery optionality makes the model difficult. Volatility choice, whether to include unauctioned bonds, and other market assumptions require care; the suggested models are frameworks, not a complete pricing recipe.
Key ideas
- Model the yields or prices of every deliverable bond over the contract’s relevant dates.
- A short-rate model or yield-factor diffusion can supply the simulated bond values.
- The futures value depends on the cheapest-to-deliver bond at each node or along each path.
- An American option can then be valued using the resulting futures tree or simulated paths.
- Ignoring timing and end-of-month delivery options simplifies the sketch but limits its realism.
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# Pricing an american style option on a bond future # Pricing an american style option on a bond future what is the good way to pricing american option on bond future? From bonk fixed income securities 3rd by Tuckman, I understand how to pricing European option on bond future, but I still have no clue how to pricing american option. ## Answer by Helin (score 4) https://quant.stackexchange.com/a/11542 Pricing a bond futures contract is already a very difficult task (because of the embedded delivery option), not to mention an American option on it. Bottom line, you'll need to build either a tree/lattice or run some monte carlo simulations. Here's a sketch of how you could go about doing it – 1) Using a term structure model, generate the distribution of the yields/prices of all the deliverables between the price date and the last delivery date. You may want to have time slices on at least the spot settlement date, some potential exercise dates, the last trade date of the futures, the first delivery date, and the last delivery date. The term structure model can be as simple as a short-rate model (e.g., Vasicek or Hull-White) and you can build trees/lattices following standard literature. The model can be calibrated using either on-the-run bonds or cheapest-to-delivers. In practice, however, many people diffuse bond yields directly (Tuckman alluded to it in his book) – starting from today's spot yields, you can use 2-3 principal component factors to diffuse the yields into the future. 2) Once you have a grid of bond deliverable prices, you can price the bond futures contract using backward induction. If you ignore the end-of-month option (bond futures expire one week before the last delivery date) and timing option (bonds can be delivered any time between the first delivery date and the last delivery ate), you could assume that delivery happens on the last delivery date. In this case, it's trivial to see which bond should be delivered on each node in a tree or path in a MC simulation (the cheapest one). This allows you to compute the bond futures' price throughout the grid. 3) Finally, given the bond futures tree/lattice/MC simulated paths, it should be straightforward to price the option on the bond futures. These models can be super complex. The delivery option part is particularly tricky and you should work closely with market makers with regard to the assumptions. For example, what volatility should you use to calibrate the model; do you want to model unauctioned bonds too; etc. ## Answer by Probilitator (score 2) https://quant.stackexchange.com/a/10809 American Options are a tricky subject and pricing them is almost never easy. A lot depends on the model etc. Assuming you that you a familiar with monte carlo and that you know the risk neutral dynamics of your porcess - you could use monte carlo least squares. The paper on the topic is easily accesible and not too technical. Suggested reading: Valuing American Options by Simulation: A Simple Least-Squares Approach
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