What is psi and when should I worry about dividend sensitivity?

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AcadiFi · Accepted Answer

Psi (sometimes written as phi) measures option sensitivity to the continuous dividend yield q. For a European call, ψ_call = -S·T·e^(-qT)·N(d1); for a put, ψ_put = S·T·e^(-qT)·N(-d1). Call psi is negative: higher dividends reduce the forward price and therefore lower the call value. Put psi is positive. Psi mirrors rho structurally — both scale with T and depend on cumulative normals — but acts on the underlying's growth rate rather than the discount rate.

Example: Vurham Telecom call, S = $65, K = $70, q = 3.5%, T = 1.5, d1 = 0.12, N(0.12) ≈ 0.548. Psi = -65·1.5·e^(-0.0525)·0.548 ≈ -50.7 per 1.00 change in q, so a dividend-yield increase of 50 bps cuts call value by about $0.253.

Practical use: desks trading dividend swaps or equity derivatives on high-yield names like utilities and REITs must hedge psi separately. Variance swap pricing models at institutions such as Kelwin Structured Products include psi to manage the impact of projected dividend schedules. For FRM, psi is less frequently tested than the primary Greeks but appears in questions about employee stock options (where dividends paid by the company reduce option value) and in stock-index options where the basket yield shifts seasonally. Don't confuse psi with the secondary Greek 'speed' (third derivative w.r.t. S), which tests differently.

What is psi and when should I worry about dividend sensitivity?

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