Jelly roll (options)

Disregarding interest on dividends, the theoretical value of a jelly roll on European options is given by the formula:

${\displaystyle JR={\frac {K}{1+r_{1}\cdot t_{1}}}-{\frac {K}{1+r_{2}\cdot t_{2}}}-D}$

where ${\displaystyle JR}$ is the value of the jelly roll, ${\displaystyle K}$ is the strike price, ${\displaystyle D}$ is the value of any dividends, ${\displaystyle t_{1}}$ and ${\displaystyle t_{2}}$ are the times to expiry, and ${\displaystyle r_{1}}$ and ${\displaystyle r_{2}}$ are the effective interest rates to time ${\displaystyle t_{1}}$ and ${\displaystyle t_{2}}$ respectively.[5]

Assuming a constant interest rate, this formula can be approximated by

${\displaystyle JR=K\cdot (t_{2}-t_{1})\cdot r-D}$.[5]

This theoretical value ${\displaystyle JR}$ should be equal to the difference between the price of the call time spread (${\displaystyle CTS}$) and the price of the put time spread (${\displaystyle PTS}$):

${\displaystyle CTS-PTS=JR}$.[5][1]

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.[5]

• Box spread (options)
• Butterfly (options)
• Rolling (finance)
• Straddle