Futures Generalization

Making the following changes to (1)(A), we can generalize the mechanism to serve futures markets:

1. Replace X by nX (notional)

2. Similarly to nX introduce nY

3. Rename to $L_d$ $L_{nX,d}$ and similarly $L_{nY,d}$

4. Perform (3) for $A_d$

5. From (1)(A) omit points 4 through 7

6. Pricing occurs as follows:

   a. $P_{X/Y,d} = \frac {A_{nY,d}} {A_{nX,d}}$

   b. $P_{Y/Y,d} = \frac {1} {P_{X/Y,d}}$

7. For any transaction of ‘u’ units of nX at ‘d’, the following occurs:

   a. $L_{nX,d} \pm u;$ implying $↻_{z =d_{min}}^d (A_{nX,z} \pm u)$

   b. $L_{nY,d} \pm { u \times P_{X/Y,d} };$ implying $↻ _ {z = d_{min}} ^ d [A _ {nY,z} \pm {𝑢 \times P _ {X/Y,d}}]$

   c. opposing signs as above are used to update ‘nX’ and ‘nY’