I'm reading a paper (Statistical arbitrage in the U.S. treasury futures market 2017), and have come across this derivation for the price of a bond future assuming interest payments and coupons compound continuously:

bond pricing derivation

I am confused by the formula for the coupon payments. Why is there a negative sign in front of the coupon rate? This formula shouldn't include the par value of the bond being repaid back, as it matures at T1 + 10 years. However, at t=T1, the formula gives K, which is additionally confusing.

Can someone explain how the author derived this expression for the value of the continuous coupon payments at time t?

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    $\begingroup$ Possible duplicate of Formula for forward price of bond $\endgroup$ – Helin May 2 '19 at 0:55
  • $\begingroup$ Not only I cannot understand that formula $K e^{-c(T_1-t)}$ I think it may be wrong. $\endgroup$ – Alex C May 2 '19 at 1:46
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    $\begingroup$ I don't agree that it is a duplicate question BTW. It is different because of the "continuous coupon payments" asumption. $\endgroup$ – Alex C May 2 '19 at 15:15
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    $\begingroup$ A polite Email to Wale Dare econpapers.repec.org/paper/usgeconwp/2017_3a16.htm asking for clarification may be in order. $\endgroup$ – Alex C May 2 '19 at 17:00
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    $\begingroup$ Just sent a message; however that math appears to me to just link the price of the future F to the spot price of the bond B so that equation 3.2 may follow. All further analysis just relies on eq. 3.2 alone, so I'm not sure this mysterious equation for the value of the continuous coupon payments really matters much in the context of what this paper is trying to demonstrate. $\endgroup$ – npp1993 May 2 '19 at 19:35

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