Yield Trading Generalization

Making the following changes to (1)(A), we can generalize the mechanism for yield trading:

  1. Replace X with PTx; PTx is the principal component of a given yield-bearing asset X

  2. Retain steps (2) through (6)

  3. Bootstrap by setting iXd=RxxAd;iX_d = R_x x A_d; where RxR_x is the staking APR; and then update by creating (+) / deleting (-) iX as APR changes: ±ΔiXd=±ΔRxxAd\pm \Delta iX_d = \pm \Delta R_x x A_d

  4. Point 7 is reframed as follows:

    a. For any transaction of u'u' PTx maturing at d'd', the following occurs:

    b. Ld±u;L_d \pm u; implying z=dmind=(Az±u)↻_{z =d_{min}}^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=yield payment due at t on principle uC_t=yield\ 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'

  5. Pricing occurs as follows:

    a. PPTx/X,d=1(1+Yd)(d/365)P_{PTx/X,d} = \frac {1} {(1 + Y_d)^{(d / 365)}}

    b. PYTx/X,d=1PYTx/X,dP_{YTx/X,d} = 1 - P_{YTx / X,d}

  6. Yields are defined as follows

    a. YPTx,d=YdY_{PTx,d} = Y_d

    b. 𝑌𝑌𝑇𝑥,𝑑𝑌_{𝑌𝑇𝑥,𝑑}: Solve t=dmind[C(1+YYTx)(𝑡/365)]PYTx/X,d=0\sum _ {t = d_{min}} ^ {d} [ \frac {C} {(1+Y _ {YTx}) ^ {(𝑡/365)}} ] − P _ {YTx/X,d} = 0 for YYTx;Y _ {YTx}; where CC is the daily yield on a unit of X; and 'd' is denominated in days.

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