Can anyone help clear this up for me? I got this Topic Test question wrong and the answer does not make sense to me. Below is the Vingette text, followed by the answer choices, followed by the explanation. I would think that because Callable bond value increases as interest rate volatility decreases, the OAS would decrease due to it being apart of the denominator in the present value equation ) and vice versa for putable bonds)
Scahill then asks, “While we are on the topic of OAS, a question that comes to mind is how the interest rate volatility assumption impacts the OAS of callable and putable bonds.” Morgan responds, “It is my understanding that as interest rate volatility declines, the OAS for callable bonds decreases while the OAS for putable bonds increases.”
Q. Is his response to Scahill’s question regarding the impact of changes in interest rate volatility on the OAS of callable and putable bonds, Morgan is most likely:
- incorrect about callable and putable bonds.
- correct about callable bonds and incorrect about putable bonds.
- correct about putable bonds and incorrect about callable bonds.
Solution
A is correct. Morgan’s response to Scahill is incorrect. As interest rate volatility declines, the embedded call option becomes cheaper; thus, the higher the arbitrage-free value (or model value) of the callable bond.
Callable bond value = Value of straight bond – Value of call option
A higher value for the callable bond means that a higher spread needs to be added to one-period forward rates to make the arbitrage-free bond value equal to the market price (i.e., the OAS is higher). For putable bonds as interest rate volatility declines, the value of the put option declines as does the arbitrage-free value of the putable bond.
Putable bond value = Value of straight bond + Value of put option
This implies that a lower spread needs to be added to one-period forward rates to make the arbitrage free bond value equal to the market price. Thus, in this instance, the OAS is lower.