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Post-Trade Elastic BULL and BEAR Claims

· 20 min read
Eric Forgy
Founder of CavalRe

Multiswap's Post-Trade Elasticity Model gives every token a reserve, a scale, and a marginal price. This article asks whether the same structure can support two directional claims associated with a Reserve Asset:

  • BULL, whose return exceeds the Reserve Asset's return when that return is positive and falls more when it is negative;
  • BEAR, whose return has the opposite sign and may have greater than one-for-one short exposure.

The accounting must come first. BULL and BEAR are both positive claims against the pool, so both are credit accounts. They are economically opposite because their prices respond differently, not because their ledger polarities differ. Once that distinction is fixed, double-entry accounting and post-trade value-flow conservation reduce the claim problem to a small system of exact finite equations.

The resulting research model has a general form for any homogeneous elasticity. When price elasticity and scale elasticity both equal one half, the claim solve becomes quadratic. A constant relative-claim elasticity κ\kappa remains optional: κ=2\kappa=2 gives a particularly symmetric log-return geometry, while κ>2\kappa>2 is necessary if both BULL and BEAR must have greater than one-for-one exposure.