On This Page
- What is the volatility risk premium?
- How is the volatility risk premium calculated?
- Worked example
- How the volatility risk premium becomes a dollar payoff
- How to align implied and realized volatility windows
- How traders use the volatility risk premium
- Limitations of the volatility risk premium
- Bottom line
- FAQ
Key Takeaways
- Use the sign convention implied minus expected realized volatility when estimating the premium at entry.
- After the window closes, implied minus subsequently realized volatility measures the realized spread.
- The worked 20% implied and 15% realized pair gives a spread of 5 volatility points.
- Squaring the decimal inputs gives a variance spread of 0.0175, equivalent to 175 variance points.
- Calculate the selected strategy’s dollar payoff from its contracts, quantities, entry prices and hedge transactions.
What is the volatility risk premium?
The volatility risk premium (VRP) is the compensation embedded in volatility pricing, measured as option-implied volatility minus the volatility expected to be realized over the same future horizon. A positive premium means options are priced for more movement than is expected to occur. At entry, the estimate compares option-implied volatility with the expected realized volatility for that horizon.
After the horizon ends, compare the entry implied value with the volatility actually realized. This completed spread provides a record of the pricing-versus-outcome difference.
How is the volatility risk premium calculated?
Entry IV of 20% and subsequent realized volatility of 15% give a +5-volatility-point spread. In variance units, 0.20² minus 0.15² equals 0.0175. Multiplying by 10,000 converts it to 175 variance points.
At realized volatility 20%, both spreads are zero. At 28%, the volatility spread is −8 points and the variance spread is −384 points. For each individual pair of nonnegative volatilities, the two differences share a sign.
Formula
Realized volatility spread = entry IV − subsequent RV. Realized variance spread = entry IV² − subsequent RV². Entry variance-premium estimate = implied variance − expected realized variance.- Match the underlying, start and end dates, annualization and volatility conventions.
- Use decimal volatilities when calculating decimal variance differences.
- Multiply decimal variance by 10,000 to express it in variance points.
- The entry estimate uses an expected future value; the realized spread uses the completed observation window.
- For one pair of nonnegative volatility values, squaring preserves the sign of their difference.
Worked Example
Record entry implied volatility of 20% for one 30-calendar-day horizon. Compare three subsequent realized-volatility outcomes for that same window: 15%, 20% and 28%.
- At 15% realized: volatility spread = 20 − 15 = +5 points; variance spread = 0.20² − 0.15² = +0.0175, or +175 variance points
- At 20% realized: both spreads equal zero
- At 28% realized: volatility spread = 20 − 28 = −8 points; variance spread = 0.20² − 0.28² = −0.0384, or −384 variance points
- For a short variance contract struck at 400 variance points with $100 variance notional, these settlement differences are +$17,500, $0 and −$38,400
The realized spread changes with the completed observation window. A specified variance contract converts the variance-point difference directly into dollars. For listed options, calculate the full option and hedge ledger to obtain the trading result.
How the volatility risk premium becomes a dollar payoff
A short variance contract struck at 400 variance points with $100 per variance point notional receives $17,500 when realized variance is 225. It pays $38,400 when realized variance is 784.
Listed-option strategies use their own cash flows and sensitivities. A delta-hedged option book, a covered call and a cash-secured put have different payoff structures. Calculate the result from the contracts actually held.
How to align implied and realized volatility windows
Use the same underlying and start and end dates. Match the annualization and observation conventions. A calendar-day option horizon contains its own number of trading sessions; count those sessions directly.
Record the entry volatility expectation separately from the subsequently observed result. Evaluate a series of trades using the same units and window convention.
How traders use the volatility risk premium
Inspect the term structure, skew and event calendar. Use options flow to examine the selected contracts, then compare their entry premiums.
The options profit calculator then compares the price, time and IV scenarios for the chosen structure and quantity.
Limitations of the volatility risk premium
- Record the entry estimate and score it when the window closes. The entry premium compares implied volatility with an expected realized value, and the realized spread is measured over the completed window.
- Size short-volatility trades for a negative window. The premium can turn negative in any window: at 28% realized volatility, the worked spread is −8 points and the short variance contract pays $38,400.
- Match the conventions: the same underlying, start and end dates, annualization and session count. Mismatched windows produce a misleading spread.
- Calculate a listed-option strategy’s profit from the contracts actually held. The spread measures pricing; listed-option strategies have their own cash flows, hedges and costs.
Bottom line
The volatility risk premium measures how much volatility the options market prices in compared with what is expected or later realized. Estimate it at entry with matched windows and units, record the completed spread afterward, and judge any strategy built on it by its own payoff, including the windows where realized volatility exceeds the implied level.
Clear answers
Frequently Asked Questions
Sources and Further Reading
- Cboe: White Paper Shows Volatility Risk Premium Facilitated Higher Risk-Adjusted Returns for PUT Index
- CFA Institute: How Well Does the Market Predict Volatility?
- OIC: Volatility and the Greeks
How entries are sourced, calculated and updated: editorial methodology.