Redemption & Valuing longZCB tokens

Fixed Term Instruments

A user can redeem longZCB at maturity. Redemption prices are calculated as the following

$$RedemptionPrice = max(1 -(loss/s_l), 0)$$

where s_l denotes the supply of longZCB and loss denotes the loss incurred by the instrument. If loss is 0, the redemptionPrice is 1.

Perpetual Instruments

A user can redeem longZCB anytime there is withdrawable liquidity in its underlying instrument. Redemption prices are calculated as the continuously priced value of the instrument's junior tranche, as illustrated in tradable tranches. At a high level, its pricing equation can be simplified down to the following

$$longZCBPrice =juniorValue = \frac{(totalAssets - (seniorValue * s_s))}{s_j}$$

In words, it is the leftover asset after all senior supply s_s has redeemed for seniorValue. seniorValue is the value accrued to the passive investors of VT, and can be computed via the following equation,

$$seniorValue = inceptionPrice * \prod_t(1+promisedReturn_t)$$

inceptionPrice refers to the starting price of longZCB tokens, and promisedReturn_T refers to the per second compounded rate of promised return for senior holders at time T. Intuitively, the higher the instrument's yield is compared to the promisedReturn_T, the more valuable longZCB becomes.

The P&L realized for the manager would be

$$longZCBAmount * (longZCBPrice_{i+1} - longZCBPrice_{i})$$

Detailed derivations and explanations for the pricings are in the whitepaper