Bond Dealer Generalization

In section 1.A we showed the way Temporal works with zero-coupon borrowing and lending, here we generalize it to work with any bonds. With coupon bonds there is a stream of interest payments before the principal is repaid at maturity, rather than all interest + principal being paid at maturity.

Additionally, in the bond dealer context, we treat a bond sale as a borrow and bond purchase as a lend transaction. There would be a separate AMM pool dealing bonds of a given issuer, e.g. ‘US Treasury’. We take the example of one such pool below:

Making the following changes to (1)(A), we can generalize the mechanism to deal in bonds:

  1. Retain points 1 through 6

  2. Point 7 is reframed as follows:

    a. For any transaction of 'u' face value / principal maturing at ‘d’, the following occurs:

    b. Ld±u;L_d \pm u; implying 𝑧=𝑑𝑚𝑖𝑛d(Az±u)↻ _ {𝑧 = 𝑑𝑚𝑖𝑛} ^ {d} (A_z \pm u). where, ↻ represents function iterates itself from minmin to maxmax value (here, dmin through dd_{min}\ through\ d).

    c. Define Ct=coupon payment due at t on principle uC_t = coupon\ payment\ due\ at\ t\ on\ principle\ u

    d. 𝑡=dmind𝑧=𝑑mint(iXz±Ct)↻ _ {𝑡 = d_{min}} ^ d ↻ _ {𝑧 = 𝑑 _ {min}} ^ t (iX_z \pm C_t)

    e. ±\pm are determined by table (1)(B) titled 'Transaction Impact'

  3. Point (8) will be adapted as follows:

    When a bond is bought / sold by the AMM, each of the bond’s payments (principal u and interest cprincipal\ 'u'\ and\ interest\ 'c') at ‘t’ are discounted at ‘Yt’ and the whole bond is valued as sum of all discounted payments

    a. Value of bond as per AMM = t=dmind[Ct(1+Yt)(𝑡/365)]+[u(1+Yd)(d365)]\sum _ {t = d_{min}} ^ {d} [ \frac {C _ t} {(1 + Y _ t) ^ {(𝑡/365)}} ] + [ \frac {u} {(1 + Y_d) ^ {(\frac {d} {365})}} ] where ‘t’ and ‘d’ are denominated in days

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