What it means
Start with a synthetic forward, which is a long call and a short put at the same strike and expiry. Together they behave like owning the underlying asset and paying the strike price on the expiry date.
A jelly roll uses two of these, one at a nearer expiry and one at a later expiry, with opposite signs. In the usual convention, a long jelly roll is long the synthetic forward at the later expiry and short the synthetic forward at the earlier expiry.
The share price exposure cancels out, since each position moves with the share in the opposite direction. What remains is the cost of carrying the position between the two dates, meaning interest on the strike price less any dividends expected in the period.
Because it isolates carrying costs, the jelly roll is useful to market makers and arbitrage desks. It can be used to lock in a financing rate, to check whether option prices are consistent with interest rates and dividends, or to roll a position from one expiry to another at a known cost.
Individual investors rarely use it, because it involves four option legs and trading costs. The idea can be understood through put-call parity, the relationship that links call prices, put prices, the share price and the present value of the strike.
When parity holds, the difference between the two synthetic forwards depends only on interest and dividends. If the market price of the roll differs from that value, traders may see an arbitrage opportunity, subject to costs and risks such as early exercise.
Naming conventions vary between trading desks, so a long jelly roll to one trader may be called short by another. The legs, strikes and expiries should always be written out explicitly.
This entry explains the common version, and it is not trading advice.
In practice
Real-world examples.
Example
A market maker sees that the roll between two expiries is priced below the value implied by short-term interest rates. She buys the roll and hedges the remaining risks. She expects to profit as prices move toward fair value.
Example
A hedge fund holds a synthetic long position that expires next month and wants to move to a later expiry. It trades a jelly roll to move the position at a known cost. The share price exposure stays the same.
Example
A bank trader checks whether the roll implies a sensible financing rate. He finds that it implies a borrowing cost well above the market rate. He investigates whether the difference reflects a high cost of borrowing the shares or a pricing error.
Formula
Calculation
Jelly roll value = (Call - Put at the later expiry) - (Call - Put at the earlier expiry)
With no dividends, a synthetic forward costs Share price - Present value of strike, so the roll equals the strike discounted at the interest rate between the two dates:
Roll = Strike x (e^(-r x T1) - e^(-r x T2))
For a strike of $100, an interest rate of 5% a year, an earlier expiry of 0.25 years and a later expiry of 0.5 years, a simple approximation is $100 x 0.05 x 0.25 = $1.25. The exact calculation is $100 x (0.98758 - 0.97531) = about $1.23. So the long roll costs roughly $1.23 per share, or $123 for a standard contract of 100 shares.Case study
Seen in the real world.
Quillfeather Securities is an illustrative, fictional trading firm that operated a desk for index options. A trader noticed that the March to June roll at a strike of 4,000 implied a financing rate about 0.4 percentage points above the short-term borrowing rate.
On a strike of 4,000, a financing difference of 0.4% a year, held for a quarter of a year, is worth about 4,000 x 0.004 x 0.25 = 4 index points per contract unit. The trader bought the roll and hedged the interest rate exposure with futures. Over the next few weeks, the implied rate drifted back toward the market rate and the position made a small profit.
The firm's risk manager reminded the team that the trade carried costs, margin requirements and the risk of early exercise on American-style options. The story is illustrative, but it shows that a jelly roll is a trade about financing and not about the direction of the market.
Watch out
Common mistakes.
- Thinking the strategy is a bet on the share price, when its value comes from interest and dividends between the two expiries.
- Assuming all desks use the same naming, when long and short jelly roll can be reversed.
- Ignoring trading costs, which can wipe out the small edge that most jelly roll trades offer.
Questions
People also ask.
What is a jelly roll in options?
It is a combination of two synthetic forward positions with different expiries and the same strike, one long and one short.
Why would anyone trade a jelly roll?
Traders use it to lock in financing costs, to test option prices against interest rates, or to roll a position between expiries.
Does a jelly roll have price risk?
It has very little direct exposure to the share price, but it can be affected by interest rate changes, dividend changes and early exercise.
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