Interpreting Instantaneous Drift Inferred from Option Greeks

Summary

The post examines a formula from a paper on European option pricing that expresses instantaneous mean drift using a call’s vega, delta, and gamma. The author compares the formula with current option prices and finds negative estimates, despite reading the paper as suggesting positive drift for equity markets. They also question the claim that the drift parameter should remain constant across strikes sharing an expiration, since a simple check appears to contradict it.

The document is a question about interpreting a theoretical relationship, not a resolved explanation. It gives no numerical market data, derivation, or answer identifying whether the issue lies in the formula, assumptions, units, or implementation. Its useful lesson is that a parameter inferred from option Greeks depends on the model’s precise definitions and assumptions, and that qualitative claims about a constant parameter should be checked against the framework before being applied to market prices. The post alone does not establish how to estimate drift robustly or whether the observed results invalidate the paper’s formulation.

Key ideas

• The cited pricing formulation relates instantaneous drift to a European call’s vega, delta, and gamma.
• The author reports negative drift estimates from market prices, conflicting with their reading of the paper’s equity-market discussion.
• The author questions whether the parameter should be constant across strikes for one expiration.
• The post provides no resolution, derivation, or empirical evidence sufficient to diagnose the discrepancy.

Tags

# Mean instantaneous drift from option prices


# Mean instantaneous drift from option prices












I'm going through the paper "Pricing European Options in Realistic Markets" by Schaden (2002) as its formulation for instantaneous mean drift seemed really interesting.

On page 14, the author says that it can be expressed via greeks for any European-style call:

α = - (call_vega - 0.5*call_delta + 0.5*call_gamma) / call_delta

However, from current market prices, I'm getting negative drift, and the paper seems to frequently imply that this drift is positive. That is, constant α > 0 qualitatively reproduces the volatility smile and term structure often observed in equity markets. (For α=0, everything is reduced to BSM's assumption of constant volatility.)

Furthermore, it implies that this α is constant across strikes within a particular expiration, but this is also negated by a simple test case.

Is it possible that I'm completely misinterpreting the above equation and, if so, what am I missing?

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