The two legs

Every Kappis series locks stock tokens in a vault and issues two position tokens against them. This page walks through the three primitive operations — split, subscribe, merge — and the payoff math that ties the legs together.

Split

Deposit n stock tokens; receive n Income and n Upside. Free, permissionless, available while the series is in its Created or Open state, bounded only by per-transaction and per-series unit caps and by vault integrity.

n stock tokens ──► vault lock ──► n Income + n Upside

Why the legs are a covered call, taken apart

Locking one stock token gives you exactly this payment capacity: everything below K, plus everything above K. Split it in two and you have a covered call decomposed into its components:

| Settlement price S | Income receives | Upside receives | Total | | --- | --- | --- | --- | | S ≤ K (say $200, K = $235.63) | min(S, K) = $200 | $0 | $200 = one token | | S > K (say $300, K = $235.63) | K = $235.63 | S − K = $64.37 | $300 = one token |

Whatever happens, the legs sum to the underlying. That identity is enforced by the vault — not by a peg, not by an oracle, not by an admin.

Subscribe

Subscribing is a split with one extra step: the newly minted Upside is consigned directly to the series' auction. You keep the Income, and your Upside sits in the auction's lot pool waiting to be sold for a premium.

  • When subscribing you set a reserve step (0–239): your lot will not sell below that step's price. Step 239 means "sell even at the floor".
  • While the auction has not started (or after a failed round), you can unsubscribe and redeem.
  • After the auction clears, your net premium (95% of proceeds) can be claimed at any time — it never expires.

Merge (Recompose)

burn n Income + n Upside ──► redeem n stock tokens
  • Any moment, any series state, free, permissionless.
  • This is the protocol's anchoring invariant: if the legs trade for less than one stock token, anyone buys both and merges; if they trade for more, anyone splits and sells. Arbitrage pins the legs to the underlying.
  • The only exception: if the token issuer destroyed vault collateral, redemptions scale pro-rata by vault balance / issued units — the same fair-share rule that governs settlement (see Settlement & claims).

A full epoch, worked out

Setup: NVDA, P0 = $224.41, cap +5% → K = $235.63. Alice splits 1 unit and subscribes her Upside; the auction clears at $2.20 per unit. Alice's net premium after the 5% protocol fee is $2.09.

| Settlement S | Alice (Income) receives | Bob (Upside) receives | Bob P&L | | --- | --- | --- | --- | | $200 | 1.0 token ≈ $200 + $2.09 | 0 | −$2.20 | | $230 | 1.0 token ≈ $230 + $2.09 | 0 | −$2.20 | | $300 | 0.7855 token ≈ $235.63 + $2.09 | 0.2145 token ≈ $64.37 | +$62.17 |

Check any row: eI + eU = 1.0 token exactly. The vault is always whole.