# 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? Oct 13, 2015 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. Oct 13, 2015 at 17:36
• It makes sense for single-stock futures. Just subtract the present value of the expected dividend.
– amsh
Oct 13, 2015 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). Oct 13, 2015 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 Oct 14, 2015 at 18:39