How do dividends affect equity options and futures pricing, and what risks arise from incorrect dividend forecasts?

Dividends are a critical input in equity derivative pricing because they reduce the forward price of the stock. Incorrect dividend forecasts create pricing errors in options and futures that can lead to unexpected profits or losses, particularly for long-dated positions.\n\nImpact on Forward Price:\n\nForward with discrete dividends:\nF(0,T) = S(0) x e^{rT} - Sum(D_i x e^{r(T-t_i)})\n\nForward with continuous dividend yield:\nF(0,T) = S(0) x e^{(r-q)T}\n\nHigher expected dividends -> lower forward price -> lower call values and higher put values.\n\nDividend Impact on Options:\n\n| Factor | Call Options | Put Options |\n|---|---|---|\n| Higher expected div | Decreases value | Increases value |\n| Surprise div cut | Increases value | Decreases value |\n| Surprise div hike | Decreases value | Increases value |\n| Ex-date stock drop | Delta loss (if long) | Delta gain (if long) |\n\n`mermaid\ngraph TD\n A[\"Thornton Industries
S = $120, Div = $2.00
Ex-date in 15 days\"] --> B{\"Dividend Surprise?\"}\n B -->|\"Div cut to $1.00\"| C[\"Stock drops less
than expected on ex-date
Forward rises ~$1.00\"]\n B -->|\"Div raised to $3.00\"| D[\"Stock drops more
than expected on ex-date
Forward falls ~$1.00\"]\n C --> E[\"Call gains ~$0.55
Put loses ~$0.45
(delta-weighted)\"]\n D --> F[\"Call loses ~$0.55
Put gains ~$0.45\"]\n`\n\nWorked Example:\n\nA market-maker at Ashwick Securities prices a 6-month ATM call on Thornton Industries ($120):\n\nUsing expected dividends of $2.00 (discrete):\n- Forward = $120 x e^{0.05 x 0.5} - $2.00 x e^{0.05 x (0.5-0.04)} = $120 x 1.0253 - $2.00 x 1.0230 = $123.04 - $2.05 = $120.99\n- BSM call price with this forward: $6.42\n\nIf dividend is unexpectedly cut to $1.00:\n- Forward = $123.04 - $1.00 x 1.0230 = $123.04 - $1.02 = $122.02\n- New BSM call price: $7.05\n- Loss for a short call position: $7.05 - $6.42 = -$0.63 per share\n\nFor 1,000 contracts (100,000 shares), the loss is $63,000 from a single dividend surprise.\n\nDividend Risk Exposures:\n- Rho_div (dividend sensitivity): measures how option value changes per $1 dividend change; approximately -e^{-r(T-t)} x N(d1) for calls\n- Long-dated options have more dividend risk because more dividends occur before expiry\n- Stock replacement strategies (using deep ITM calls instead of stock) must account for forgone dividends\n- Futures-options parity: American call early exercise is driven by dividends --- if the dividend exceeds the remaining time value, early exercise is optimal\n\nEarly Exercise Decision:\nAn American call should be exercised just before the ex-date if:\nD > C(S, K, T-t_ex) - C(S-D, K, T-t_ex) + K x (1 - e^{-r(t_ex)})\n\nThis simplifies to: exercise when the dividend exceeds the time value of the option minus interest savings.\n\nPractice dividend-adjusted option pricing in our CFA Derivatives question bank.