Volatility Risk Premium (VRP) Decomposition

Overview

The Volatility Risk Premium (VRP) is the persistent tendency for option-implied volatility to exceed subsequent realized volatility. Advanced quantitative funds decompose the VRP into its constituent, orthogonal components (moneyness, term structure, and correlation) to target structural inefficiencies driven by non-economic flows, moving beyond the simple selling of insurance.

Key Concepts

• VRP — The difference between the market's pricing of future variance under the risk-neutral measure (ℚ) and the expectation of variance under the physical measure (ℙ).
• Moneyness Decomposition — Isolating the pure variance premium (ATM) from skewness (Third Moment) and kurtosis/tail risk (Fourth Moment).
• Term Structure Decomposition — Isolating short-term mean-reverting tactical flows (Gamma) from long-term structural hedging flows (Vega).
• Correlation/Dispersion — Isolating the Correlation Risk Premium (CRP) by trading index volatility against its constituents.
• Vanna (∂Δ / ∂σ) — The sensitivity of an option's Delta to changes in volatility, driving mechanical dealer flows that can suppress volatility.
• Charm (∂Δ / ∂t) — The sensitivity of Delta to time decay, creating structural bids as options approach expiration.

Formulas

Key Takeaways

• The VRP is highly asymmetric. "Bad Variance" (downside) carries a persistent premium, while "Good Variance" (upside) can often be negligible due to overwriting supply.
• The ultimate goal of VRP decomposition is to construct a "Barbell" portfolio: harvesting the high-frequency core VRP (income), hedging the jump risk (protection), and using dispersion (alpha) to fund the protection leg.
• Pure ATM variance strategies are heavily influenced by Gamma flows, while downside skew is dominated by crash aversion from pension funds and insurers.

Related Reading

• Decomposing the Volatility Risk Premium: A Sophisticated Framework for Structural Arbitrage
• Watch on YouTube