What Is Epsilon2?
Last reviewed: by Options Analysis Suite Research.
Epsilon2 is the second derivative of option value with respect to the dividend yield (partial2 V / partial q2). It is the convexity of option value in dividend-yield space, analogous to how gamma is the convexity in spot space. Epsilon2 is a higher-order dividend Greek used in advanced dividend-risk analytics for high-yield equities and long-dated index options.
What Is Heston Epsilon2?
Epsilon2 captures the curvature of option value as a function of dividend yield. A long call has negative epsilon (calls lose value when dividend yield rises) and small positive epsilon2 (the rate of value loss accelerates slightly with rising yield). The magnitude is small per 1% yield change but compounds for large yield shifts or for portfolios with concentrated dividend-yield exposure.
Two intuitions for epsilon2. First, epsilon2 is the analog of vomma in dividend-yield space - both are second-order convexity measures of their respective first-order Greeks. Second, epsilon2 matters mainly for large-dividend-yield shifts (e.g., dividend cuts of 50%+ from regulated utilities or financial-stress-driven dividend suspensions).
Why Does Epsilon2 Matter?
For most retail options trading, epsilon2 is too small to track explicitly. It becomes operationally relevant in three contexts. First, dividend-cut risk modeling. When a high-yield stock is at risk of dividend cut, the dividend yield's distribution becomes wide, and epsilon2 captures the convexity correction to a linear epsilon estimate of the impact.
Second, structured products with embedded dividend exposure. Convertible bonds, accelerated share repurchase agreements, and other structures have dividend exposure that is non-linear in the dividend rate. Epsilon2 is part of the standard Greek set for those products.
Third, index options across multi-dividend-cycle tenors. SPX 1-year and 2-year options have dividend exposure that compounds; epsilon2 is the convexity correction.
How Heston Computes Epsilon2
In production, epsilon2 is computed by central second-difference on the Heston pricer: (V(q+h) - 2 V(q) + V(q-h)) / h^2 with h typically 25 basis points. Closed-form epsilon2 from differentiating Heston twice with respect to q exists but is rarely used in production due to numerical-stability tradeoffs.
Related Greeks
Epsilon2 is the second-order dividend Greek. Its first-order partner is epsilon (or RhoQ in Heston context). Higher-order analogs in spot, vol, and time directions include gamma, vomma, and second-order time Greeks.
Related Concepts
Epsilon · RhoQ · Heston Model · All 17 Greeks
References & Further Reading
- Hull, J. C. (2022). Options, Futures, and Other Derivatives, 11th ed. Pearson.
- Gatheral, J. (2006). The Volatility Surface. Wiley.
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This page is part of the 17 Greeks reference covering every options Greek with formula, intuition, worked example, and how each pricing model computes it. Browse the full documentation.