Simple Numerical Example

Instead of submitting proposed interest, the utilizer would instead submit proposed expected returns.

As an example, given that the current market price of ETH/USD is 1000, a market maker(utilizer) could propose 4 1-week call option buys for strike prices 1050, 1100, 1150, and 1200(VT and longZCB in this instance would have its numeraire be ETH, so the options would be covered), at (example)prices 10, 5, 3, 1 USD per contract, respectively.

Managers will purchase longZCB tokens on any strikes that he deems have a favorable risk-adjusted return(such that the covered calls are not exercised). Let's assume that the strike price with the most amount of bought longZCB is 1100.

An Instrument contract would allow the market maker and the protocol to perform an OTC for these synthetic 1100 ETH/USD strike calls, such that the collateral would be collected by the winner after maturity. Let's assume 100 of these swaps were made, so the collateral posted by the market maker would be 100 * 5 = 500 USD. Now, the proposed principal and expected returns would be

Proposed Principal: 100ETH

Proposed Expected Returns: 500USD = 0.5ETH

Proposed Duration: 1 week

Assuming there is only one manager that bought 10 longZCB at an average price of 0.98(computed via the equations in section 7 of the whitepaper), with posting 9.8 ETH as collateral. Let's study the outcome of 2 possible events

1. 1 week has passed, and the current market price for ETH is 1060. The redemption price of longZCB token is max(1-0/10 ,0) = 1. The manager has gained 10-9.8 = 0.2 ETH.

2. 1 week has passed, and the current market price for ETH is 1130. Loss per ETH would be (1130-1100)/1130 = 0.0265ETH. The redemption price of longZCB token is max(1- 0.0265*100/10, 0) = 0.735. The manager has lost 9.8-7.35 = 2.45 ETH.

Although the example illustrates a case for one manager, in practice it would require at least 3 managers and a certain amount of total collateral posted by the managers to fund a strike price. Exact payoffs would differ from different parameters.