Free lesson · Crypto derivatives

Inverse contracts pay in the base asset

Open interactive lessonPractice calculationsExplore labs

An inverse contract has a fixed quote-currency face amount but pays its price-change result in base tokens. Reciprocal prices are therefore essential.

For the simplified inverse payoff, a long receives the difference between the base-token value of quote face amount at entry and at exit. A rise in price yields positive base-token P&L.

Dollar value of the profit depends on the conversion price used. Base collateral itself also changes in dollar value, so an inverse derivative and a linear derivative with similar face value have different total account exposures.

Apply it in a strategy

• Audit inverse-contract hedge units and collateral currency exposure.
• Record the input timestamp, executable quantity, currency and horizon. Reconcile the result with a cash-flow or state table.
• Stress this failure condition: Using the linear formula for an inverse contract misstates both settlement units and path exposure.

Research deliverable

Build and explain a inverse contracts pay in the base asset worksheet. Audit inverse-contract hedge units and collateral currency exposure.

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.

# Python 3.10+; standard library unless NumPy is imported below.
# Inputs and outputs use the units defined in this lesson. Synthetic teaching example.
def inverse_pnl(face_usd,entry,exit_price):
    if min(entry,exit_price)<=0: raise ValueError("Positive prices required")
    base=face_usd*(1/entry-1/exit_price)
    return base,base*exit_price

print(inverse_pnl(10000,50000,55000))