Free lesson · Arbitrage

Start with every possible payoff

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Two portfolios are equivalent only if they deliver the same cash in every relevant state at the same time. Equal average returns are insufficient.

Create one row per terminal outcome, including void or default when permitted. A statistical tendency to converge is different from a contractual identity.

A certain payment above its purchase price still has to cover the time value of capital. Compare payoff and funded cost at the same date.

Apply it in a strategy

• Prove complete-set or replication payoffs before calling a price difference arbitrage.
• Record the input timestamp, executable quantity, currency and horizon. Reconcile the result with a cash-flow or state table.
• Stress this failure condition: A void, default or incompatible settlement state can destroy equivalence.

Research deliverable

Build and explain a start with every possible payoff worksheet. Prove complete-set or replication payoffs before calling a price difference arbitrage.

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 3.10+; standard library unless NumPy is imported below.
# Inputs and outputs use the units defined in this lesson. Synthetic teaching example.
def state_surplus(payoffs,holdings,cost,rate,years):
    if not payoffs or years<0 or any(len(row)!=len(holdings) for row in payoffs):
        raise ValueError("Aligned states and holdings required")
    return [sum(q*x for q,x in zip(holdings,row))-cost*(1+rate*years) for row in payoffs]

print(state_surplus([[1,0],[0,1]],[1,1],.96,.04,.5))