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. $L_d \pm u;$ implying $↻ _ {𝑧 = 𝑑𝑚𝑖𝑛} ^ {d} (A_z \pm u)$. where, ↻ represents function iterates itself from $min$ to $max$ value (here, $d_{min}\ through\ d$).

   c. Define $C_t = coupon\ payment\ due\ at\ t\ on\ principle\ u$

   d. $↻ _ {𝑡 = d_{min}} ^ d ↻ _ {𝑧 = 𝑑 _ {min}} ^ t (iX_z \pm C_t)$

   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 ($principal\ 'u'\ and\ interest\ 'c'$) 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 = $\sum _ {t = d_{min}} ^ {d} [ \frac {C _ t} {(1 + Y _ t) ^ {(𝑡/365)}} ] + [ \frac {u} {(1 + Y_d) ^ {(\frac {d} {365})}} ]$ where ‘t’ and ‘d’ are denominated in days