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 LdL_d LnX,dL_{nX,d} and similarly LnY,dL_{nY,d}

  4. Perform (3) for AdA_d

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

  6. Pricing occurs as follows:

    a. PX/Y,d=AnY,dAnX,dP_{X/Y,d} = \frac {A_{nY,d}} {A_{nX,d}}

    b. PY/Y,d=1PX/Y,dP_{Y/Y,d} = \frac {1} {P_{X/Y,d}}

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

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

    b. LnY,d±u×PX/Y,d;L_{nY,d} \pm { u \times P_{X/Y,d} }; implying z=dmind[AnY,z±𝑢×PX/Y,d]↻ _ {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’

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