# Confirmation of interest rate volatility vs. changes

Hi guys, I studied Reading 54 today and jotted down some very brief notes. I’d like to put it into my book but just want to ensure it’s accurate (because it’s based on my deductions rather then being directly stated). Can someone please confirm and let me know if all is correct? Thank you! Interest rate VOLATILITY up = Vcall up, Vnoncallable unaffected, therefore Vcallable down While NONcallable bonds are not affected by interest rate volatility, they ARE affected by interest rate changes (inverse relationship). Therefore, as interest rates go up, Vcallable down, Vcall down, Vnoncallable down.

1. Correct 2. Correct 3. Correct
1. Correct 2. Correct 3. Kinda correct. ------> Interest rates go up, Value callable goes down (because bond prices are inversely related to interest rates AND the value of the call goes up which reduces the callable bond, so you got two things going here), Value call goes up (who owns the call? the issuing company), Value noncallable goes down. Don’t confuse with “volatility” of rates increasing and “interest rates” increasing. These are two different things, but can happen simultaneously. Best in June!

Yes, missed out on Vcall in the 3rd point. Vcall will go up. Totally agree with david.

i asume the call is bond option here. if yes then with int rates up the value of the call goes down. underlying, the bond, goes down, the call option goes down.

okay i see what u are saying. lets go back to put call parity to get value of call option. C = P + S - X/ (1+r) If interest rates go up, last component goes down and C goes up. But with interest rates going up, S the spot price comes down(intrinsic characteristic of the underlying in this case). So, C goes down. since these are contradicting effects, look like we cannot predict the value of embedded call option with interest rate movements then.

interesting, lets have a look at this: S = F / (1+r) , where F is forward price of a bond when rates go up (parallel shift pls), forward price goes down. rewrite the parity: C = P + (F - X)/(1+r) the difference is discounted by higher rate so the PV up, but F will be probably higher amount than the difference therefore the effect will be that it all goes down. On top of that time to expiry will be probably shorter than bond tenor from expiry time. btw, P will go up (do not forget about put value) but the delta of put option is lower (in abs) than delta of S (or F)

davidyoung@sitkapacific.com Wrote: ------------------------------------------------------- > 1. Correct > 2. Correct > 3. Kinda correct. > ------> Interest rates go up, Value callable > goes down (because bond prices are inversely > related to interest rates AND the value of the > call goes up which reduces the callable bond, so > you got two things going here), Value call goes up > (who owns the call? the issuing company), Value > noncallable goes down. > > Don’t confuse with “volatility” of rates > increasing and “interest rates” increasing. These > are two different things, but can happen > simultaneously. > > Best in June! Either you are wrong or Schweser is wrong. See question below: Wall now turns his attention to the value of the embedded call option. How does the value of the embedded call option react to an increase in interest rates? The value of the embedded call: A) decreases. B) increases. C) remains the same. Your answer: A was correct! Since the underlying asset to the option (the bond) decreases in value the option must decrease in value also. (Study Session 14, LOS 54.e, f)

As the risk free rate increase the price of a call option increase. the price of a PUT option decreases. the value of the bond would decrease: Vbond = vnoncallable - vcallable as vcallable increases, vbond decreases. Am I off on this, I thought this was an area I had down pretty well so I think I’m right.

VCallableBond=VNonCallAbleBond - VCall. Interest Rate increase - VNonCallableBond decreases. VCall Increases (as above) so VCallableBond decreases VPutableBond = VNonPutableBond + VPut VNonPutableBond decreases VPut Decreases as well. So VPutableBond decreases.

CPK-- Your claim is the when rates increase, Vcallable and Vnoncallable decrease and Vcall increase. The answer to the Schweser question says that Vcallable and Vnoncallable decrases, and Vcall decreases as well. Are you saying they are wrong?

Yes, Vbond = Vnoncallable - Vcall … that is what I meant. I agree Vcall should increase due to an increase in Int rates.

bought callable bond is equal to bought straight bond and sold call option (sold right to buy the straight bond). the value of the straight bond goes down when rates go up. therefore the value of the call bond option decreases. or the probability that the issuer exercises the option (calls the bond) goes down when rates go up. when probability of exercise goes down the value of option goes down ok?

C=S+P-x/(1+r) as r increases x decreases and C increases… ok?

and what happens with S in the formula? (it changes with rate change too!) pls see my second post in this thread, I was explaining rate change effect on parity (of bond option) there.

Look at Exhibit 27 in reading 60 on page 208 of volume 6. I obviously can’t draw it here, but it shows the relation b/w Option price and Rho. You can see from the graph that as the risk free interest rate rises the call otion price increases. I agree that when the underlying price decreases the price of the call decreases as is explained by delta. The question then is: how large delta is compared to rho? From the graph in the book it would seem that rho would have a larger impact on C than Delta. anyone know for sure? Also, the book just specifies the underlying as any investment, however in the case here with bonds where prices move inversely to int rates it seems that some investments may not react the same way as others.

Ok, so I found an “unofficial” answer to this: For calls on Bonds the Delta drowns out the Rho effect - So pfcfaaf’s reasoning is true. The graph in the book is for equity securities, though it doesn’t mention that in the book. In fact I don’t remember reading anything on the differences b/w eq/bond options; does anyone have any reference to this in the CFAI texts? or would this not be tested? Iwould think that if there’s a prectice Q like the one above it may be tested after all. TenTen - BTW both answers are correct b/c for an equity call an increase in int rates would still increase the value of the equity call, however as was just posted with a rise in int rates the value of a call on a bond decreases.

So the answers conflict?! Derivatives section tells us that as rates increase, rho causes the value of the call (and put) to increase slightly. Fixed Income section tells us that as rates increase, the Value of the callable bond decreases and consequently, the value of the call on that bond decreases. As Schweser says in their answer: Since the underlying asset to the option (the bond) decreases in value the option must decrease in value also. (Study Session 14, LOS 54.e, f) Can someone please make sense of this conflict?

it is part of LEVEL 1 see Level 1 CFAI book 5 page 243