Exchange rate probability distributions derived from option prices
- Author:
- Vetle Øye Opheim and Jonas Tendal
- Series:
- Staff Memo
- Number:
- 2/2026
Summary
Option prices can contain information regarding the market's pricing of the probability of price movements of an option's underlying instrument. Using options with many redemption rates, it is also possible to estimate a probability distribution for the price of the underlying asset.
In this Memo, our calculations are based on the method used by the Atlanta Federal Reserve Bank in its Market Probability Tracker, adapted to be used with FX options. Based on the estimations in this Memo, it appears that a larger probability of a considerable NOK depreciation against USD and EUR is usually priced into the market compared with the probability of a corresponding appreciation.
Options market-based probability distributions also have some limitations. Options are priced to ensure that there is no considerable possibility of arbitrage between the options market and forward market so the expected value of the distributions will usually be close to the market forward rate with the same maturity. As a rule, we must also assume that the distributions contain both market expectations and risk premiums as it is currently not easy to distinguish between them.
Staff Memos present reports and documentation written by staff members and affiliates of Norges Bank, the central bank of Norway. Views and conclusions expressed in Staff Memos should not be taken to represent the views of Norges Bank.
ISSN 1504-2596 (online)