# Forward contract pricing of coupon paying security

PLease help me in understanding how to price forward contract for coupon paying security. For instance if we get into a contract to buy a security in next six month whose coupon due in next two month. So how to price it. Please provide me an intuitive understanding of this.

• Buy something that starts in 6 months but pays a coupon in 2 months? Are you sure you know what you're talking about? – SmallChess Oct 13 '15 at 14:22
• @StudentT: the question of user86354 is not weird like you suggest it is. You can enter into a forward contract to buy an asset 6M from now, independent if that asset pays a dividend/coupon in the mean time. For example a forward on a bond, or a div paying stock. – mbison Oct 13 '15 at 17:36
• It makes sense for single-stock futures. Just subtract the present value of the expected dividend. – amsh Oct 13 '15 at 17:36
• What amsh says and without more information there is little more you can say. I'd close it but maybe someone wants answer it? An illustration would be nice (hint). – Bob Jansen Oct 13 '15 at 19:31

(This answer is broadly in line with the comment of Amsh. I added it because Amsh his 1 line solution says substract the PV (present value) of the div; However, the example below shows that one should substract the FV (future value) of the div). edit: to be more precise future value from moment you receive div, until you deliver the stock.

Assume $S(0) = 100$ is the price of asset at time 0. You enter into a forward agreement to deliver the stock at time T = 12 months for K.

Assume the rate $r$ is fixed. Assume there is one dividend payment Q = 5 at time T_coup = 2 months.

You borrow S(0) dollars and buy 1 stock. At t=2/12 you receive 5, these you invest in the money market against rate r.

at time T = 1 you deliver your stock. You receive K. Your dividend has grown to 5*exp(r*10/12). Your initial loan is repayable 100*exp(r*12/12).

The deal is fair if K + 5*exp(r*0.5) = 100*exp(r*1). K = 100*exp(r*1) - 5 exp(r*10/12)

Also see: https://www.ma.utexas.edu/users/mcudina/m375t_lecture_six_forward_prices.pdf equation 6.1

• welcome. happy to help – mbison Oct 14 '15 at 18:39