Free lesson · Crypto derivatives

Linear contract payoff and the multiplier

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A linear derivative pays in the quote currency in proportion to the underlying price change and signed exposure.

Positive quantity means long and negative means short. Multiply contract count by base units per contract before applying the price change. Record whether settlement uses an index, mark or final trade price.

Initial margin is collateral, not the notional traded and not necessarily the maximum possible loss. Fees may apply to notional on entry and exit rather than to posted margin.

Apply it in a strategy

• Translate orders into correct exposure and separate the derivative result from margin deposits.
• Record the input timestamp, executable quantity, currency and horizon. Reconcile the result with a cash-flow or state table.
• Stress this failure condition: Wrong multipliers or a different settlement currency can change P&L by orders of magnitude.

Research deliverable

Build and explain a linear contract payoff and the multiplier worksheet. Translate orders into correct exposure and separate the derivative result from margin deposits.

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 linear_pnl(contracts,base_multiplier,entry,exit_price):
    if base_multiplier<=0 or min(entry,exit_price)<=0: raise ValueError("Positive multiplier and prices required")
    return contracts*base_multiplier*(exit_price-entry)

print(linear_pnl(-10,.01,50000,48000))