Skip to content
All library documents

Pricing a Forward on a Coupon-Paying Security

Article Quant Q&A · Author: manish
Read the original

Summary

The document explains how an interim coupon affects the no-arbitrage delivery price of a forward contract. Its example assumes a security worth 100 today, a one-year delivery date, a coupon of 5 paid after two months, and a fixed continuously compounded rate. The replicating strategy borrows the purchase price, buys the security, and invests the coupon until delivery.

At delivery, the coupon investment offsets part of the loan repayment, so the forward price equals the financed spot value minus the coupon’s value grown from its payment date to delivery. This is why the relevant deduction is the coupon’s future value at the delivery date, rather than its present value at contract initiation. The example assumes a single known coupon and a fixed rate; it does not address uncertain payments, changing rates, or other carrying costs.

Key ideas

  • A forward on a coupon-paying security must account for coupons received before delivery.
  • The coupon is reinvested from its payment date through the forward delivery date.
  • The fair delivery price is financed spot value minus the coupon’s accumulated value at delivery.
  • The example assumes a known coupon and a fixed interest rate.

Tags

Fixed incomeDerivatives pricing
Full text
# Forward contract pricing of coupon paying security


# 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.

## Answer by mbison (score 3)

https://quant.stackexchange.com/a/21201

(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

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.