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Asian Options

Options whose payoff depends on an average price.

Reviewed 2026-08-10TheQuantBateman ResearchReading note
01Intuition

Read the contractual cash flows first.

Averaging dampens the impact of one extreme fixing and better matches gradual physical exposure.

ONE-LINE DEFINITION

Options whose payoff depends on an average price.

02Mathematics

Express payoff and present value precisely.

max⁡(1n∑iSti−K,0)\max(\frac1n\sum_i S_{t_i}-K,0)
Notation and units

Decimal rates and volatilities, year-fraction time and continuous compounding unless stated otherwise.

03Assumptions

Make conventions part of the contract.

01

Contract dates, calendars, settlement, notionals and payoff currency are part of the valuation input.

02

Discounting and projection conventions must match the collateral and quotation framework.

03

The displayed payoff omits legal terms and lifecycle events unless stated otherwise.

“An unstated convention is a future reconciliation break.”— THEQUANTBATEMAN
04Market use

Locate the quote and replication instruments.

Commodity procurement, production and revenue hedging.

Intuition→Mathematics→Implementation→Desk risk
05Desk view
FRONT OFFICE VIEW

Map cash-flow changes into hedge risk.

Reconcile the contractual payoff before reading the COMM risk. Small date or convention changes can move cash flows before any model parameter moves.

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06Related

Continue to the nearest instrument or model.