Estimating closeout value on a Treasury bond options strangle

Estimating the position before entry

The archive uses a short options strangle made from two U.S. Treasury bond futures options as the case for estimating the position's future value before entry. The position is an options strangle: a short put-and-call combination that collects premium if the underlying futures stay inside a chosen band and that must later be bought back to exit.

That pre-trade estimate is built around three changing inputs at once: movement in the underlying futures price, option time decay, and shifts in volatility.

How the sold legs are locked in

After a large decline in bonds, the sold call in the case uses an 118 strike instead of 120. That choice raises the call premium and narrows the underlying range that still keeps the strangle profitable. The extra credit is a trading-range premium: extra credit taken by selling a closer call after a large decline, paid for with a narrower band in which the strangle can remain profitable.

The put leg is set as a 110-strike futures option against June T-bond futures, with a T-bill interest rate, a calculation date, and the option's expiration date. The listed put price of 51/64 is entered so implied volatility can be solved rather than supplied as an input.

The 118-strike call is copied across later columns, and implied volatility is solved for each option before any scenario fields are changed. Implied volatility is the volatility that makes a pricing model match an observed option premium and that then becomes the baseline for later scenario columns.

Date and price scenarios two months forward

Two later column pairs move the calculation date two months forward and compare an underlying price inside the intended range with a price outside that range.

Those altered columns are recomputed with the Black-Scholes model to produce theoretical put and call values under the new date, price, and volatility assumptions. The Black-Scholes model is the pricing engine used to restate each leg after the planner changes remaining time, the underlying price, or volatility.

Reading the output as closeout value

The theoretical values are read as the prices at which the two legs would have to be purchased to close the strangle if those conditions occurred. That buy-back price is the closeout value: the theoretical price at which each sold leg would have to be purchased to unwind the strangle under a stated future date, price, and volatility. The in-range pair is treated as the more favorable closeout.

Volatility can be overwritten as its own what-if input. The same layout can be extended beyond two options, and a worksheet figure is shown as a planning aid for alternative scenarios.