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Complete-set purchases and redemption

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Start with the idea

One share of every exhaustive, mutually exclusive outcome pays one collateral unit in total. The price comparison must use all executable asks and redemption costs.

Symbols, units & horizon
  • N: complete sets bought
  • m: exhaustive outcome count
  • a_i: executable ask in USD per $1 outcome share
  • C: total costs USD
  • Π: modeled complete-set surplus USD
  • common collateral and settlement assumed

When and why to use this

Audit within-condition set economics with a payoff table, collateral checks and fill limits.

One share of every exhaustive, mutually exclusive outcome pays one collateral unit in total. The price comparison must use all executable asks and redemption costs.

In the binary model, YES pays one when the condition is true and NO pays one otherwise. Buying both creates the same modeled payout in both states.

A protocol may allow merging a full set before resolution, but access, fees, collateral denomination and contract version must be checked. Never apply the one-dollar identity to a collection of unrelated headlines.

Π=N(1−∑i=1mai)−C
Model assumptions, derivation and arithmetic

Complete-set purchases and redemption

  1. Enumerate states and verify exactly one outcome pays one in every state.
  2. Sum the acquisition asks per complete set.
  3. Subtract acquisition cost from the fixed payout, scale by sets and subtract costs.
Work it by hand

YES ask .47 and NO ask .50 cost .97 per set. For 200 sets, payout $200 minus $194 purchase and $2 costs leaves $4.

Apply it in a strategy

  • Audit within-condition set economics with a payoff table, collateral checks and fill limits.
  • Record the input timestamp, executable quantity, currency and horizon. Reconcile the result with a cash-flow or state table.
  • Stress this failure condition: A missing outcome or inconsistent void rule invalidates the fixed payout; partial fills leave outcome exposure.

Research deliverable

Build and explain a complete-set purchases and redemption worksheet. Audit within-condition set economics with a payoff table, collateral checks and fill limits.

Evidence boundary: Synthetic arithmetic and scenarios illustrate mechanics. They are not historical returns, a paper replication, or evidence of an executable edge. Research sources and their access limitations are recorded at the end of this module.

Research sources, review dates and limitations

Python implementation

Self-contained teaching example. Python 3.10+; dependencies and input conventions are shown in the code and notation. Run in your own Python environment.

# Python 3.10+; standard library unless NumPy is imported below.
# Inputs and outputs use the units defined in this lesson. Synthetic teaching example.
def complete_set(asks,sets,cost):
    if not asks or any(not 0<=a<=1 for a in asks) or min(sets,cost)<0: raise ValueError("Invalid complete-set inputs")
    return sets*(1-sum(asks))-cost

print(complete_set([.47,.50],200,2))

Continue learning

Prediction Strategies: Logic, Sizing and Market Making — all lessons
  1. Complete-set purchases and redemption
  2. Subset relations and executable bounds
  3. Bounds for joint and union events
  4. Binary Kelly sizing and estimation error
  5. Decision buffers for probability uncertainty
  6. Quoting revenue and adverse selection
  7. Event overlap and portfolio variance
  8. Evaluate the decision process, including failed fills

Quantitative finance and development glossary · Python resources and libraries · Research sources and limitations