# Callable bond question

Hi, I had this question on QBank regarding callable bonds and cannot figure out why I am wrong: How does the value of the embedded call option react to an increase in interest rates? A) increases B) remains the same C) decreases D) may increase or decrease I chose D). Here are my 2cts: V callable = V option free - V Call option Rates increase, so both V callable and V option free decrease. But what does prevent the volatility to increase, leading to an increase in V Call option? Thanks for telling me what is wrong.

Just like any other option (like a call or put for a stock) volatility increase the value of the option. For a callable bond, that decrease the value and for a putable bond it increases the value of the bond.

callable bond doesn’t differ much from option-free bond for large interest rates. the higher the interest rate, the lower the value of the call option. i remember a picture from level I that demonstrated that. therefore, the answer is C.

As Interest Rates increase, value of the Call option decreases and value of the Put option increases. Think Convexity/Duration Graph!! So per that logic… C should be the answer? EDIT: You guys are TGV from France… too fast

Wow, I miss read that, I thought it was asking about volatility. I’m retarded. It should be C. As interest rates increase, the price of the bond decreases, and they have no need to call the bond at a higher price.

Thanks guys, I just saw the graph flashing in front of my eyes. Indeed as rates go up, the value of the call goes down and for high rates, callable and option-free are the same. Sorry about that…and yes, aswer was C EDIT: funny you mentioned TGV as I am French…but was way slower on that one

the answer is C and the concept is fairly straight-forward, but again arguably the question is vague. interest rate could overnight rate in which case it’s irrelevent to the value of the call option on a 10 year bond… but i think you can assume it’s the interest rate/yield on the straight bond…

Actually it’s not - then the question is about the rho of the embedded option.

A) Increase in interest rates make an option more valuable since the buyer of the option (the bond issuer in this case) doesn’t have to put the full value of the exercise price up front. The value of the call option increases. Callable bond value = Straight bond value - Call option value Hence, the callable bond value decrease when the call option value increases (especially when this is combined with a decrease in the Straight bond value as is the case here)

nicolargol Wrote: ------------------------------------------------------- > EDIT: funny you mentioned TGV as I am French…but > was way slower on that one hehe… weird coincidence

olivier Wrote: ------------------------------------------------------- > A) > > Increase in interest rates make an option more > valuable since the buyer of the option (the bond > issuer in this case) doesn’t have to put the full > value of the exercise price up front. > > The value of the call option increases. > > Callable bond value = Straight bond value - Call > option value > > Hence, the callable bond value decrease when the > call option value increases (especially when this > is combined with a decrease in the Straight bond > value as is the case here) So you own a bond call and you want interest rates to increase…

WTF is going on here?

Joey - that’s what I’m sayin’…can you shed some light and give me the proper answer, so as not to convolute me even further?

Best answer: maratikus Wrote: ------------------------------------------------------- > callable bond doesn’t differ much from option-free > bond for large interest rates. the higher the > interest rate, the lower the value of the call > option. i remember a picture from level I that > demonstrated that. > > therefore, the answer is C.

The answer is C. Think of the call option like you do a mortgage. Say rates rise. Will you refinance? probably not b/c you already locked in a lower rate. Call option is analogous to the option to refi your mortgage. From the issuer perspective, the issuer wont call the bond b/c they are paying you less than the market.

Those last two are fine answers.

Chris, monkey & Joey - thanks

i thought of the rho as one person mentioned, but that doesn’t come into binomial model and even if you used some sort of modified BS for call value, i’m pretty sure the change in straight price would swamp the rho (and i’m thinking they go in same direction anyway)…

actually i was thinking about the wording. the value of the call option to the company goes down, that’s for sure. but from the perspective of the investor: value callable = value straight - value call straight goes down, value call goes down, but it has a negative sign, so the value to the investor actually went up from having the call option… but i’d say they’re asking you to say that when interest rates, go up the value of a call option on a bond goes down. common sense wording, but they can get tricky.