# putable bond volatility

In comparing the price volatility of putable bonds to that of option-free bonds, a putable bond will have: A) more price volatility at higher yields. B) less price volatility at low yields. C) more price volatility at low yields. D) less price volatility at higher yields.

A.

high yield = high volatility on both Puts and Calls.

puttable bond will have very small volatility and small duration for high yields for low yields puttable bond will be very similar to option-free bond the answer is D.

High yield>> Low price>>More likelihood of excersing the put option>>High Price volatility. A?

Agree with maratikus: D If you have a bond you can sell back at par, and yields rise such that it trades at a discount, you just sell it back at par. So the put “puts” a floor under the price.

I answered A, which is incorrect The answer is D: The only true statement is that putable bonds will have less price volatility at higher yields. At higher yields the put becomes more valuable and reduces the decline in price of the putable bond relative to the option-free bond. On the other hand, when yields are low, the put option has little or no value and the putable bond will behave much like an option-free bond. Therefore at low yields a putable bond will not have more price volatility nor will it have less price volatility than a similar option-free bond.

D. higher yield, the curve will be pushed up ( or price will be more stable) since people are exercising their options ( think of everybody exercising thus the price will be the same -strike price). thus less volatility.

Is it D?? Low Duration at high yields because of the FLOOR (put price) in place - Dinesh S

I always look at it as: price = option free bond price + put option premium or: price = option free bond price - call option premium In this case, yields going up causes the option free bond price to go down, but the put option premium goes up. The put option premium rising offsets some of the option free price change causing less volatility. I will probably confuse more people than I help by posting that, but if I help anyone it will be worth it I guess. When I get these questions, I always go back to those formulas to help.

moto376 Wrote: ------------------------------------------------------- > I always look at it as: price = option free bond > price + put option premium > or: price = option > free bond price - call option premium > Yes moto376, thats a better (more mechanical) way of remembering this concept [and that’s how I do it usually], atleast better than visualizing the graph that Schweser decided to put up on their cover page of Book-4 - Dinesh S

The easiest way to think about these questions is to imagine the yield curves in your mind. Because the price of the putable bond is bound by a floor equal to the strike price, the yield curve of the puttable bond will become flatter relative to the option-free bond as rates increase. The flatter the yield curve, the less sensitive. Equally, just imagine the worst case scenario. The price of the bond is equal to the strike price. No mater how much higher rates go, the price of the bond will not fall (because its not difficult to see the immediate arbitrage oppurtunity this would present itsself- assuming American style options)

Mr Moto 376, can you explain why rise yield increases put premium? i understand using put-call parity, C+X/(1+r)n=S+p, P=C+x/(1+r)n-S If r rise, then X/(1+r)n decline, cause P decline… I know this maybe stupid, please help me with this…

but when R declines, S goes up as well… I had gone with this same approach some time ago, and was told to just remember – Put and call prices GO UP when Interest rates GO UP. Directly proportional to Interest rate volatility… then pcb = pncb - c --> when r goes up, C goes up, pncb goes down, so Callable bond is much more volatile. ppb = pnpb + p --> when r goes up, P goes up, pnpb goes down, so there is an offsetting effect between pnpb and P – so putable bond is not as volatile.

I think D too