Mechanism: defining pair volatility before a worked example
Pair volatility is a way to describe how much the exchange rate of a currency pair moves within a selected time period. The phrase “volatility” is used in different ways, so a worked example must state the exact method.
A practical approach is to pick:
- Time window: e.g., 10 trading days.
- Price measure: e.g., the quoted pair price (such as “X units of currency B per 1 unit of currency A”).
- Volatility metric: for example, range-based volatility (max minus min), percent-change volatility (relative movement), or a returns-based metric (such as standard deviation of daily percent returns).
Because these choices change the numeric result, “pair volatility” alone does not uniquely determine a number.
Direct answer: what a worked example looks like
A worked example of pair volatility shows the calculation step by step and lists every assumption. Here is one self-contained scenario using a range-based definition (often easier to verify).
Worked example (assumptions stated)
Assumption A1 (data): Over a chosen window, the currency pair’s quoted price takes the following daily values (arbitrary but consistent with the definition):
- Day 1: 1.2000
- Day 2: 1.1950
- Day 3: 1.2050
- Day 4: 1.1980
- Day 5: 1.2100
- Day 6: 1.2060
- Day 7: 1.2010
- Day 8: 1.2070
- Day 9: 1.2090
- Day 10: 1.2030
Assumption A2 (window length): The volatility is calculated over exactly these 10 days.
Assumption A3 (metric): We define range-based volatility as the absolute difference between the maximum and minimum quoted prices in the window.
Step 1: identify max and min
- Maximum price = 1.2100 (Day 5)
- Minimum price = 1.1950 (Day 2)
Step 2: compute range
- Range = 1.2100 − 1.1950 = 0.0150
Step 3 (optional but common): express as a percentage One simple way is to divide by the window’s minimum (any consistent base is an assumption):
- Percent range (relative to min) = 0.0150 / 1.1950 ≈ 1.26%
Result
- Range-based pair volatility over the 10-day window = 0.0150
- Percent-range volatility ≈ 1.26%
This worked example is “verifiable” because another reader can recompute max, min, and the subtraction using the provided values.
Evidence or example: how the same pair can yield different “volatility” numbers
Even with the same 10 days of prices, a different volatility metric produces a different result.
Comparison by metric (both are still “worked examples”)
- Range-based volatility depends only on the max and min values. If outliers appear, they dominate the result.
- Returns-based volatility uses how each day changes from the previous day. Two windows can have the same range but different day-to-day variability.
Assumption B1: Keep the same 10 daily prices as above.
If you switch to a returns-based approach, you must also state:
- Return definition (e.g., simple percent return from Day t−1 to Day t).
- Aggregation (e.g., compute standard deviation of those returns).
- Annualization or no annualization (if you scale results, that scaling is another assumption).
Because those details are not automatic, “pair volatility” should always be treated as “volatility measured using a specific method over a specific window.”
Limitations and risks: what can go wrong with volatility calculations
- Choice-of-definition risk: A range-based number and a returns-based number are not interchangeable; they answer different questions.
- Window sensitivity: Changing the time window can materially change the result, especially when volatility clusters.
- Market regime change: Historical variability may not resemble future variability; the relationship is not guaranteed.
- Execution reality: If volatility is later used to interpret risk, realized outcomes can differ due to trading costs, spreads, and latency—factors that are not included in the simple price-only example.
- Failure mode from outliers: Range-based volatility can jump sharply when a single spike creates a new max or min.
Verification or next question: how to independently check pair volatility
To verify a worked example, recompute from the written assumptions:
- Confirm the window length and the exact price values used.
- Recalculate max and min (for range-based volatility).
- Re-check the formula (absolute range vs percent relative to a stated base).
A useful next question is: Which volatility metric matches your purpose—range, returns dispersion, or something else—and what assumptions does it require?