Sample Questions
Question 1
Easy
A callable bond exhibits negative convexity when:
Solution
B is correct.
A callable bond exhibits negative convexity when interest rates are low and the call option is near or in the money. In this region, as rates fall further, the issuer becomes increasingly likely to call the bond, limiting the bond's price appreciation. The price-yield curve bends downward (concave shape) rather than upward (convex shape), creating negative convexity. The price is compressed near the call price.
A callable bond exhibits negative convexity when interest rates are low and the call option is near or in the money. In this region, as rates fall further, the issuer becomes increasingly likely to call the bond, limiting the bond's price appreciation. The price-yield curve bends downward (concave shape) rather than upward (convex shape), creating negative convexity. The price is compressed near the call price.
Question 2
Medium
The bootstrapping method is used to derive:
Solution
C is correct.
Bootstrapping is a method for deriving the spot rate (zero-coupon) curve from the yields of coupon-paying bonds. The process works iteratively: starting with the shortest maturity bond (which gives the first spot rate directly), each subsequent bond's coupon payments are discounted using previously derived spot rates, and the final spot rate is solved for. This produces a complete spot rate curve from observed par bond yields.
Bootstrapping is a method for deriving the spot rate (zero-coupon) curve from the yields of coupon-paying bonds. The process works iteratively: starting with the shortest maturity bond (which gives the first spot rate directly), each subsequent bond's coupon payments are discounted using previously derived spot rates, and the final spot rate is solved for. This produces a complete spot rate curve from observed par bond yields.
Question 3
Hard
Using Exhibit 1, the arbitrage-free value of Bond A today is closest to:
Solution
A is correct. Work backward through the tree. At each Time-1 node the bond's remaining cash flow is the Time-2 coupon plus par, , discounted one year at that node's rate; the resulting value is then compared with the 101 call price.
Upper node: which is below the call price of 101, so the issuer does not call and the node value stays at 100.478.
Lower node: which exceeds 101, so the issuer calls and the node value is capped at 101.
Adding the Time-1 coupon of 5 to each node value and discounting the risk-neutral expectation at :
The dealer's offer of 103.55 is above this model value.
Upper node: which is below the call price of 101, so the issuer does not call and the node value stays at 100.478.
Lower node: which exceeds 101, so the issuer calls and the node value is capped at 101.
Adding the Time-1 coupon of 5 to each node value and discounting the risk-neutral expectation at :
The dealer's offer of 103.55 is above this model value.
