What it means
In everyday options trading, "rolling" means closing one contract and opening another to keep a position alive. Rolling forward moves it to a later expiry, whereas rolling backward moves it to an earlier one.
Traders do this to bring a view forward in time, to collect premium sooner or to shorten their exposure. Rolling to an earlier date is less common than rolling forward, because most traders want more time, not less.
It tends to be used when an event, such as an earnings announcement or a central bank decision, is expected before a later contract expires. It can also reduce the length of time capital is at risk.
The second meaning comes from valuation. To value an option or a project that depends on uncertain events, analysts build a tree of possible future outcomes and then "roll back" through it.
They start with the final payoffs and calculate the value at each earlier step until they reach today. At each step, the value is the weighted average of the next two outcomes, discounted for one period.
The probabilities used are the risk-neutral ones, which are chosen so that the model prices correctly. Rolling back through a tree is how many banks value American-style options that can be exercised early.
A third, everyday use comes from accounting and planning, where a balance or forecast date may be rolled back to an earlier period to compare or restate figures. Because the phrase has several meanings, a clear statement of what is being rolled and in which direction avoids confusion.
In practice
Real-world examples.
Example
A trader holds a short option expiring in two months but expects a big announcement in three weeks. She closes it and opens a similar one expiring just after the announcement, which is an earlier date, so she has rolled backward.
Example
A bank's quantitative team values an employee share option using a binomial tree. The model rolls back from the final share prices to the present to arrive at the fair value for the accounts.
Example
A treasury analyst restates a cash forecast to an earlier cut-off date to match the period in a bank's statement. She rolls the balances backward by reversing the later transactions.
Formula
Calculation
Value at a node = [q x Value if Up + (1 - q) x Value if Down] / (1 + r)
Worked example: A two-step tree uses a risk-neutral probability q of 50% and a discount rate of 0% per step to keep the arithmetic simple. At the end of step two, an option is worth $33 or $11 after an up move from the upper node, and $11 or $9 after a down move from the lower node.
Upper node value = (0.5 x $33) + (0.5 x $11) = $16.50 + $5.50 = $22
Lower node value = (0.5 x $11) + (0.5 x $9) = $5.50 + $4.50 = $10
Value today = (0.5 x $22) + (0.5 x $10) = $11 + $5 = $16
Rolling back through the tree, the option is worth $16 today. In a real model, the discount rate would be above zero and each value would be divided by (1 + r) at every step.Case study
Seen in the real world.
Tamarind Energy is a fictional company that held options to hedge its fuel costs. In this illustrative case, the treasurer noticed that a key regulatory decision on fuel taxes would be announced on the 10th, but his hedge ran until the 30th.
He closed the existing position and opened a new hedge expiring on the 12th, so that the protection covered the announcement but not the following weeks of uncertainty. This cut the premium paid by $18,000 because the new option had less time value.
After the decision, he rolled the hedge forward again to the end of the month. The team documented both steps so that auditors could follow the logic, and the treasurer noted that each roll created transaction costs that needed to be weighed against the benefit.
Watch out
Common mistakes.
- Assuming roll backward means the same in every field. In trading it concerns expiry dates, in valuation it concerns working through a tree.
- Forgetting trading costs. Each roll involves closing one contract and opening another, with commissions and spreads.
- Ignoring changes in time value. Moving to an earlier expiry normally reduces the premium, which changes the economics of the position.
Questions
People also ask.
Is rolling backward common?
Not especially. Traders usually roll forward to gain time, so rolling backward is reserved for particular situations.
What is backward induction?
It is the technique of solving a problem by starting at the end and working back to the start, which is how option trees are valued.
How do I know which meaning is intended?
Look at the context. If options expiry dates are mentioned, it is a trading move, and if trees or models are mentioned, it is a valuation method.
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