[1] It is often used to take a position on dividends or interest rates, or to profit from mispriced calendar spreads.
[2] A jelly roll consists of a long call and a short put with one expiry date, and a long put and a short call with a different expiry date, all at the same strike price.
[1] The value of a call time spread (composed of a long call option and a short call option at the same strike price but with different expiry dates) and the corresponding put time spread should be related by put-call parity, with the difference in price explained by the effect of interest rates and dividends.
[2][1] Where this arbitrage opportunity exists, it is typically small, and retail traders are unlikely to be able to profit from it due to transaction costs.
[5] The jelly roll is a neutral position with no delta, gamma, theta, or vega.
[5][1] Disregarding interest on dividends, the theoretical value of a jelly roll on European options is given by the formula: where
[5] Assuming a constant interest rate, this formula can be approximated by This theoretical value
): If that equality does not hold for prices in the market, a trader may be able to profit from the mismatch.
[1] Typically the interest component outweighs the dividend component, and as a result the long jelly roll has a positive value (and the value of the call time spread is greater than the value of the put time spread).
However, it is possible for the dividend component to outweigh the interest component, in which case the long jelly roll has a negative value, meaning that the value of the put time spread is greater than the value of the call time spread.