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:
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?