Payoff curves

Enabling unparalleled customization through parametrization

In DIVA Protocol, payoff profiles are parametric, allowing the creation of a wide range of unique and tailored payoff profiles with different slopes, barriers, and ranges. The shape of the long payoff curve is governed by four parameters: floor, inflection, cap, and gradient.

Due to the zero-sum nature, the short payoff curve is implied via the relationship payoff(Short) + payoff(Long) = 1. Visually, the short token payoff curve is just a horizontally mirrored version of the long token payoff curve. This is illustrated in the following graphic:

Illustration: Parametric payoff curves in DIVA Protocol

The amount of long and short position tokens issued is equal to the amount of collateral held in the contingent pool, resulting in a maximum payout of 1 unit of the collateral token per long/short position token. For instance, if USDC 100 is deposited into the contingent pool, one party will receive 100 long and the other party 100 short tokens, regardless of their individual contributions.

Example long and short payoff curves that result from the parametric approach are illustrated below:

Long payoff curves

Example long payoff curves

Short payoff curves

Example short payoff curves

Payoff formula

The payoff per long token is calculated as follows (assuming 0 fees):

if (finalReferenceValue = inflection):
	payoffLong = gradient
else if (finalReferenceValue ≤ floor):
	payoffLong = 0
else if (finalReferenceValue ≥ cap):
	payoffLong = 1
else if (finalReferenceValue < inflection):
	payoffLong = gradient * (finalReferenceValue - floor)/(inflection - floor)
else if (finalReferenceValue > inflection):
	payoffLong = gradient + (1 - gradient)*(finalReferenceValue - inflection)/(cap - inflection)

As payoffLong + payoffShort = 1 (ignoring fees), the short token payoff is given by payoffShort = 1 - payoffLong.