just a quick question guys. Will the value of a non-callable bond be affected by increased volatility? Please explain your answer… thanks!

Not directly.

In general, as interest rate volatility increases, so does the interest rate with which you discount the bond cash flows… …so it should be affected… Can anyone agree/disagree?

Only the ARBITRAGE-FREE value of the non callable bond remains UNAFFECTED by interest rate volatility changes I guess one should keep this in mind while evaluating the value of Vcallable wrt interest rate volatility

Deeply skeptical…

While being volatile there will be price differences but the price itself of an option-free bond is not effected by volatility.

If you’re doing the exam on book 6, I chose that it would be affected. Still haven’t looked at what Schweser says the answer “should be.”

Most of our dealings with non callable bonds like valuing them using the interest rate tree, have been done assuming that we were using arbitrage free non callable bonds. Or in other words, we assume them to be equal to their market price, and hence free form arbitrage. So, unless it is specifically mentioned otherwise, i presume it would be safe for to assume that they are arbitrage free and therefore not affected by interest rate volatility

quant, Schweser posts a similar comment … can you explain?

quantforCFA Wrote: ------------------------------------------------------- > Most of our dealings with non callable bonds like > valuing them using the interest rate tree, have > been done assuming that we were using arbitrage > free non callable bonds. Or in other words, we > assume them to be equal to their market price, and > hence free form arbitrage. So, unless it is > specifically mentioned otherwise, i presume it > would be safe for to assume that they are > arbitrage free and therefore not affected by > interest rate volatility Huh? This doesn’t have much to do with arbitrage, interest-rate trees, etc. A bond’s value is the sum of it’s discounted cash flows. If the bond isn’t callable (or have other embedded options) the cash flows are not affected by vol. The discount rates are not directly impacted by vol either. Thus, the price of the bond is a function of two things not impacted by vol so the price isn’t impacted by vol.

I agree with you. Don’t think we need to bring the question of arbitrage here. I was just being specific by saying that arbitrage free bonds are being considered. That should be a given for us. So, as far as we are concerned, non callable bonds are not affected by volatility

JoeyDVivre Wrote: ------------------------------------------------------- > quantforCFA Wrote: > -------------------------------------------------- > ----- > > Most of our dealings with non callable bonds > like > > valuing them using the interest rate tree, have > > been done assuming that we were using arbitrage > > free non callable bonds. Or in other words, we > > assume them to be equal to their market price, > and > > hence free form arbitrage. So, unless it is > > specifically mentioned otherwise, i presume it > > would be safe for to assume that they are > > arbitrage free and therefore not affected by > > interest rate volatility > > > Huh? > > This doesn’t have much to do with arbitrage, > interest-rate trees, etc. A bond’s value is the > sum of it’s discounted cash flows. If the bond > isn’t callable (or have other embedded options) > the cash flows are not affected by vol. The > discount rates are not directly impacted by vol > either. Thus, the price of the bond is a function > of two things not impacted by vol so the price > isn’t impacted by vol. I understand your point Joey. thanks. but consider this … the construction of the arbitrage free int rate tree requires an assumption on volatility. if this volatility assumption increases, then the discount rates will increase causing the arbitrage free value of the bond’s cash flows to be lower. your thoughts …?

My point exactly. Doesn’t make any sense. Apart from Schweser, does CFAI mention that anywhere? Schweser has been away from the real world in several readings but next week I intend to answer everything the way CFAI sees it.

bevrez1 Wrote: ------------------------------------------------------- > JoeyDVivre Wrote: > -------------------------------------------------- > ----- > > quantforCFA Wrote: > > > -------------------------------------------------- > > > ----- > > > Most of our dealings with non callable bonds > > like > > > valuing them using the interest rate tree, > have > > > been done assuming that we were using > arbitrage > > > free non callable bonds. Or in other words, > we > > > assume them to be equal to their market > price, > > and > > > hence free form arbitrage. So, unless it is > > > specifically mentioned otherwise, i presume > it > > > would be safe for to assume that they are > > > arbitrage free and therefore not affected by > > > interest rate volatility > > > > > > Huh? > > > > This doesn’t have much to do with arbitrage, > > interest-rate trees, etc. A bond’s value is > the > > sum of it’s discounted cash flows. If the bond > > isn’t callable (or have other embedded options) > > the cash flows are not affected by vol. The > > discount rates are not directly impacted by vol > > either. Thus, the price of the bond is a > function > > of two things not impacted by vol so the price > > isn’t impacted by vol. > > > I understand your point Joey. thanks. but consider > this … the construction of the arbitrage > free int rate tree requires an assumption on > volatility. if this volatility assumption > increases, then the discount rates will increase > causing the arbitrage free value of the bond’s > cash flows to be lower. your thoughts > …? What arbitrage?

the arbitrage free value of the bond … using the arbitrage free int. rate tree.

So, if it is not arbitrage free, we need to add some sort of spread, so that we price it properly. I think this is beyond our scope, as determining the spread to use etc is difficult based on some random volatility assumption. We only have nominal spread, Z spread and OAS to deal with. I really think we shouldn’t be wasting time on this, at this moment.

Ah…So the question is about interest rate trees? I guess the answer is that I don’t know what kind of interest rate trees you guys are learning but simple interest rate trees don’t match bond prices obtained by discounting cash flows using spot rates so variance assumptions do affect prices. Since that might be a problem, there are “arbitrage-free” binomial pricing models that address that. You will see things like Heath, Jarrow, Morton (HJM); Black, Derman, Toy (BDT); Ho and Lee and probably a bunch of others I don’t know. That’s getting beyond the scope of CFA studies.