# Can one use options on Treasury futures to hedge a portfolio?

Can one use options on Treasury bond futures to hedge a typical fixed income portfolio? If so, how can one estimate the duration for an option on a Treasury futures contract, and taking this a step further, how would one then use the duration to determine the option's contribution to the overall portfolio duration?

Yes, it is definitely possible to do so.

With a long fixed-income portfolio, you'd typically be buying puts on treasury futures or writing calls on them (writing calls may not be feasible if you're an institutional investor due to regulatory reasons). In general, duration for long puts/short calls would be negative. However see caveats below:

Typically, you might use the Black model to price the option. The duration of an option in the traditional "bond" sense would then be the sensitivity of the option price to the interest rates (or by implication, on the Treasury future's price itself).

There is a down-side though in the Black model which assumes constant interest-rate volatility while bond futures prices usually do have a time-dependent volatility - known as the pull-to-par effect.

You can use more complex interest rate models (LMM etc) but the duration would be a more complex beast to handle.

Black-model deltas may be calculated on standard call and put options on Treasury bond futures. A naive estimate of the duration of the option would be the duration of the future times the Black delta.

• The Black-Scholes delta would be wrong as it assumes non-stochastic interest rates. The Black model would be a better assumption (even that doesn't take into account the volatility term-structure). Also delta*duration is a naive estimate as you can't really decouple the delta of a bond/bond-future option from the duration of the underlying. Aug 26, 2011 at 20:15
• You're right on the Black model, my mistake, I have changed the answer above. I agree the delta*duration is a naive estimate, but I think it would work as a first approximation. A more complex interest-rate model is definitely the "right" way to go. Aug 26, 2011 at 20:45
• To use the naive estimate, must you also multiply by the ratio of the futures price to the option price? Aug 29, 2011 at 2:08