| Days | (underlying) Treasury | Forward | |
| 0 | Price = $98.25 | ||
| 182 | Coupon = 100*5%*(1/2) = $2.50 | ||
| 270 | maturity | ||
| 365 | Coupon = 100*5%*(1/2) = $2.50 |
Forward contract
- Underlying: $1 million Treasury bond (w/ 10 years remaining to maturity)
- Underlying coupon: 5% (just after a coupon payment)
- Effective annual risk-free rate: 4%
No-arbitrage forward price
= (98.25-2.50/1.04^(182/365))*1.04^(270/365)
= 98.25*1.04^(270/365)-2.50*1.04^((270-182)/365)
= $98.6185 = $98.62
| Days | (underlying) Treasury | Forward | |
| 60 | Price = $98.25 → $98.11 | ||
| 182 | Coupon = 100*5%*(1/2) = $2.50 | ||
| 270 | maturity | ||
| 365 | Coupon = 100*5%*(1/2) = $2.50 |
Value of a long position in the 270-day forward contract on a $10 million bond
= (98.11-2.50/1.04^(122/365) - 98.62/1.04^(210/365)) = -0.77696 (per $100)
-0.77696 * $10*10^6 /$100 = -$77,697 (per $10 million)
Value of a short position in the 270-day forward contract on a $10 million bond
= +0.77696 (per $100)
+$77,697 (per $10 million)
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