Convexity on option embed bonds

CFA Level II Fixed Income
#1

Schweser on convexity calculation with trees on bonds embedding options.

Here is the Schweser:

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An analyst has constructed an interest rate tree for an on-the-run Treasury security. The analyst now wishes to use the tree to calculate the convexity of a callable corporate bond with maturity and coupon equal to that of the Treasury security. The usual way to do this is to calculate the option-adjusted spread (OAS):

A) compute the convexity of the Treasury security, and divide by (1+OAS). B) shift the Treasury yield curve, compute the new forward rates, add the OAS to those forward rates, enter the adjusted values into the interest rate tree, and then use the usual convexity formula. C) compute the convexity of the Treasury security, and add the OAS.

Your answer: C was incorrect. The correct answer was B) shift the Treasury yield curve, compute the new forward rates, add the OAS to those forward rates, enter the adjusted values into the interest rate tree, and then use the usual convexity formula.

The analyst uses the usual convexity formula, where the upper and lower values of the bonds are determined using the tree.

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So if we take the steps on the Schweser they use the OAS, thus taking out the Option, but wether it is a callable or putable bond each one of the option has an impact on convexity, isn’t it?

Thanks again,

#2

Morning guys,

Any up on this one?

Thanks,

#3

if there are puts or calls you need to recompute the tree - simple as that.

#4

Got that,

And in worst case I’ll go for the answer involving a tree recompute…

So, fundamentally, forget the option, we are going for the corporate added curvature…!

Yeah!

#5

Here are the steps, in fact we want to take out the option…WHY??? Is there a bit of CFA in you God…? Please, answer me,

Step 1: Given the assumptions about benchmark interest rates, interest rate volatility, and a call and/or put rule, calculate the OAS for the issue, using the binomial model.

Step 2: Impose a small parallel shift to the interest rates used in the problem by an amount equal to +Di.

Step 3: Build a new binomial tree using the new yield curve.

Step 4: Add the OAS to each of the 1-year f** orward** rates in the interest rate tree to get a modified tree. (We assume that the OAS does not change when the interest rates change.)

Step 5: Compute the new value for V+ using this modified interest rate tree.

Step 6: Repeat steps 2 through 5 using a parallel shift of -DI to obtain the value for V-.

Step 7: Use the formula duration = (V- + V+) / 2V0(DI).

#6

Just replace at the end the duration for convexity

#7

Which is:

((V- + V+) * 2V0) / ((DI)^2*V0)

#8

I think that you meant:

((V- + V+) − 2V0) / (DI²*V0)

#9

Waou, why did I try to slay th V0?

Thanks again Magician.

You might have an answer for the convexity calculus, why do we use the OAS? (I wont think youre the messiha:)

Leave it there if its just complification,

#10

Ok I got it… Its by taking out the option that we can get the price of it… hehe

Thanks all :wink: