Question
The State of California has issued a 5-year bond (Bond A) whose coupon rate is linked to the amount of annual rainfall at the Golden
The State of California has issued a 5-year bond (Bond A) whose coupon rate is linked to the amount of annual rainfall at the Golden Gate Bridge. Specifically, if there were Q inches of rainfall in the previous year, the coupon rate for this year will be [4 + (Q/100)] %. Now exactly 2 years have passed since the bond was issued and the second coupon has just been paid. The State of California has decided to find some way to mitigate the interest rate risk associated with Bond A. The State is issuing a 3-year bond (Bond B) with coupon rate of [7 - (Q/200)]%, where Q is the same as above. Bond A is currently trading at $107, and the prices of ordinary 3 year bonds with various coupon rates are given in the following table. What will be the no-arbitrage price of Bond B? Assume face values are $100, bonds have annual coupon payment, and that all coupon payments of all bonds fall on the same date.
Coupon rate | Current Price |
4% | $91 |
6% | $99 |
7% | $103 |
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