You are long a 6-month 100-strike call with 0.60 delta on a stock at 100. The market had priced a $1.50 dividend before expiry and the company announces $2.50 instead. With zero rates, what is your profit and loss per share and what happens to the put at the same strike?

You are long a 6-month 100-strike call with 0.60 delta on a stock at 100. The market had priced a $1.50 dividend before expiry and the company announces $2.50 instead. With zero rates, what is your profit and loss per share and what happens to the put at the same strike?

Approach: A dividend lowers the forward by its present value, so translate the change into a shift in the forward and multiply by the option's sensitivity to it.

-$0.60. An extra dividend of $1.00 lowers the forward price by its present value, which at zero rates is the full $1.00, and the call responds through its sensitivity to the forward, so the loss is 0.60*1.00 = $0.60 per share. The put at the same strike has delta -0.40 with respect to the forward and gains 0.40*1.00 = $0.40. Put-call parity ties the two: C - P falls by exactly the $1.00 change in the present value of the dividend, and 0.60 + 0.40 recovers that dollar. This is why a long-dated call position is a short dividend position whether the trader intended it or not, and why single stock desks mark a dividend curve separately from the volatility surface. On a name where the dividend is the main uncertainty, quoting the option in volatility terms hides the risk that is actually being taken.

Follow-up: The dividend increase is announced but its ex-date moves to one week after expiry. What is the P&L then?

Key concepts: dividend risk, forward price, delta, put-call parity.