Rolling a position forward means closing the contract nearing expiry and opening the matching one for a later expiry. For options, the two are rarely priced the same, even at an unchanged strike and spot. More time to expiry carries more time value. That gap is the arithmetic part of what rolling costs or credits.
Definition and Formula
Rollover, in the options case examined here, means two steps. First, close a position at the strike and expiry nearing settlement. Then open the same strike at a later expiry. The underlying and the strike stay the same; only the number of days to expiry changes.
The price gap between the two expiry dates is driven fully by time value, when spot and implied volatility are held equal. The same Black-Scholes model prices a single option. Here it runs twice, with all else held fixed except how many days remain to expiry.
Holding implied volatility equal across the two expiry dates is a simplification stated plainly here. In practice, options of other expiry dates on the same underlying often carry different implied volatility. This is called a term structure. So an actual roll’s price gap is not fully explained by time value alone.
For futures, no option-pricing model of this kind applies. The near-month and next-month future prices differ by an amount the market sets on its own. This is often described as the cost of carry, or the basis. It is not worked out with a Black-Scholes-style method. This page’s worked example is specific to options.
Rollover by itself does not change how many lots are held. The number of lots carried after a roll is whatever was carried before it. This changes only if an extra sizing decision is made at the same time.
A rollover also carries a real transaction cost beyond the price gap shown here. Brokerage and other charges apply to both the closing trade and the opening one. This site’s brokerage calculator computes that on its own.
Formula: Option price = Black-Scholes model on spot and strike and days to expiry and implied volatility and rate. Time value gap is about the price at the far expiry minus the price at the near expiry. Spot, strike, IV and rate are held equal in both.
A Worked Example
| Underlying / strike (₹) | 24,280.00 / 24,300.00 |
|---|---|
| Implied volatility | 12.5% |
| Near-expiry days remaining | 3 |
| Far-expiry days remaining | 33 |
| Near-expiry price (₹) | 106.31 |
|---|---|
| Far-expiry price (₹) | 427.60 |
| Time-value difference (₹) | 321.28 |
| Difference for one lot of 65 (₹) | 20,883.20 |
Both prices come from the same Black-Scholes engine that runs the option Greeks calculator. Only the number of days to expiry changes between them. Holding volatility and rate equal across the two expiry dates is this page’s own simplification, stated in the section below.
What This Number Tells You
The two prices state what the same strike is worth at two different amounts of time remaining. Every other input is held fixed.
That gap states how much of it is time value alone, on this page’s stated assumptions.
And What It Does Not Tell You
It does not state the price either contract will actually trade at when a rollover is placed. Only the specified formula inputs are used.
It assumes equal implied volatility at both expiry dates. Where the market prices them differently, the real gap will not match this figure.
It excludes brokerage and other charges on both legs of the roll. This site’s brokerage calculator computes those on their own. It also does not extend to futures rollover, where the price is set by the market rather than by a pricing model.
Frequently Asked Questions
Why does the later expiry cost more with all else held equal?
Because more time to expiry carries more time value in the Black-Scholes model. Spot, strike, volatility and rate are unchanged between the two calculations here. Only the days figure differs.
Does this figure predict what an actual rollover will cost?
Not exactly. It states the time-value component, under the assumption that implied volatility is the same at both expiry dates. The market does not always provide that.
Why hold implied volatility equal across the two expiry dates?
To isolate the effect of time alone. Doing otherwise would mix two other effects — time and volatility — into one number.
Does rolling a trade change the number of lots held?
No, not by itself. The lot count carried after the roll is whatever was carried before it, unless an extra sizing decision is made.
Does this apply to rolling a futures contract too?
No. Futures rollover cost is set by the market itself. It is the gap between the near-month and the next-month price. It is not worked out with an option-pricing model. So this page’s worked example is specific to options.