CFA Level 2 derivatives pricing sensitivities
Derivative sensitivities describe how a value changes when an input changes. Identify whether the case concerns a forward, swap or option, then match the input change to the correct exposure and the long or short position.
The key ideas, at a glance
Delta
Read the visual, then follow the worked example below. Use the stated case assumptions.
Illustrative worked case
change per unit
- Underlying change
- 2
- Delta-only option change
- 1.2
A long option with delta 0.60 changes by approximately 0.60 × 2 = 1.20. Gamma and other changing inputs are excluded.
| Concept | Rule or decision | Common mistake |
|---|---|---|
| Delta | For a small underlying-price move, ΔV ≈ delta × ΔS. | Reverse the exposure for a short position; check contract units and multiplier. |
| Gamma | Gamma describes how delta changes with the underlying price. | A constant-delta approximation misses curvature for larger moves. |
| Vega | Vega describes option-value sensitivity to implied volatility. | Check whether vega is quoted per percentage point or per unit of volatility. |
| Rates and time | Rho and theta isolate rate and time effects under the model’s assumptions. | A sensitivity holds other inputs fixed; actual market inputs may move together. |
01Delta
For a small underlying-price move, ΔV ≈ delta × ΔS.
Watch for: Reverse the exposure for a short position; check contract units and multiplier.
02Gamma
Gamma describes how delta changes with the underlying price.
Watch for: A constant-delta approximation misses curvature for larger moves.
03Vega
Vega describes option-value sensitivity to implied volatility.
Watch for: Check whether vega is quoted per percentage point or per unit of volatility.
04Rates and time
Rho and theta isolate rate and time effects under the model’s assumptions.
Watch for: A sensitivity holds other inputs fixed; actual market inputs may move together.
Selected 2026 study concepts. Match your preparation to your registered exam-year curriculum. These notes are not complete curriculum coverage.
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Put the method to work
One worked example, from facts to answer
Given
A long option has delta 0.60 per unit. The underlying rises by 2. Hold all other inputs fixed and ignore gamma.
Method
Estimated option-value change = 0.60 × 2 = 1.20 per unit.
Answer and interpretation
The delta-only estimate is a 1.20 gain per unit. Apply the contract multiplier separately; a short option has the opposite change.
Original independent teaching example. Assumptions are stated above; this is not an official exam question or scoring key.
Apply the framework, step by step
Read an option sensitivity table, estimate a small price change and size the exposure in consistent units. Use Derivatives for the wider forward, swap and contingent-claim valuation methods.
Before you start: Long versus short positions, option payoff versus value, underlying-price units and contract multipliers.
METHOD 01
Delta
For a small underlying-price move, ΔV ≈ delta × ΔS.
Delta is a local sensitivity, so first specify whether it is quoted per option unit, share, contract or portfolio. Multiply by the small underlying-price move using matching units, then apply the contract multiplier and number of contracts if needed. A short position reverses the exposure. The delta-only estimate holds other inputs fixed and is an approximation rather than an exact new option price.
Avoid this mistake: Reverse the exposure for a short position; check contract units and multiplier.
METHOD 02
Gamma
Gamma describes how delta changes with the underlying price.
Gamma measures the change in delta as the underlying price moves. A second-order approximation adds one half × gamma × the squared underlying-price change to the delta term. For a stated positive gamma, that curvature contribution is positive for either direction of the move. Shorting the option reverses the position’s gamma. Large moves or changes in other inputs can make a local approximation unreliable.
Avoid this mistake: A constant-delta approximation misses curvature for larger moves.
METHOD 03
Vega
Vega describes option-value sensitivity to implied volatility.
Read the volatility unit before using vega. A quote per one percentage point of volatility must be multiplied by the number of percentage-point changes, not by the corresponding decimal change. For example, movement from 20% to 22% is two percentage points. Vega does not describe sensitivity to the underlying price; applying it to a price change uses the wrong input and units.
Avoid this mistake: Check whether vega is quoted per percentage point or per unit of volatility.
METHOD 04
Rates and time
Rho and theta isolate rate and time effects under the model’s assumptions.
Theta depends on the time convention: calendar time passing and time remaining to expiry move in opposite directions. Rho isolates a rate change under the pricing model. If a question changes several inputs, use only the requested approximation and keep their conventions consistent. A delta hedge neutralizes a specified first-order exposure at that point; it does not eliminate gamma, volatility, basis or rebalancing risks.
Avoid this mistake: A sensitivity holds other inputs fixed; actual market inputs may move together.
Apply it to a different case
- New facts
- A long option has delta 0.60 and gamma 0.08 per stated underlying-price unit. The underlying rises by 2; hold other inputs fixed and use the delta-gamma approximation.
- Working
- Estimated value change = 0.60 × 2 + 0.5 × 0.08 × 2² = 1.20 + 0.16.
- Conclusion
- The estimated gain is 1.36 per option unit. Apply a contract multiplier separately; the 0.16 curvature term refines the delta-only estimate.
Original teaching case under the stated assumptions, rather than an official exam question.
Questions about this method
- Does delta predict the exact option-price change?
- No. It is a local first-order approximation holding other inputs fixed. Gamma and changes in volatility, time or rates can affect the actual result.
- How do I use vega quoted per volatility percentage point?
- Multiply by the change in percentage points. If volatility moves from 20% to 22%, the change is two percentage points, not 0.02 in that quoting convention.
- Does a delta-neutral portfolio have no risk?
- No. It neutralizes a particular first-order underlying-price exposure at a point in time. Other sensitivities remain, and delta can change as market inputs move.
Sources and curriculum scope
Official outlines establish curriculum scope. The explanations and worked examples are independent teaching material; the sources do not verify or endorse them.
- 2026 CFA Level 2 curriculum outline
- Official Level 2 format and curriculum
- 2027 CFA Level 2 curriculum outline
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