Fixed Income Securities

[sipanivishal]

Hi David, I have some doubts regard the following -

i) Para 4&5;of Tuckman (Pg- 49, Chp. 3)

ii) In page -92 (Chpt 5), Tuckman, in DV01 example talks about change in the value of the option per unit change in the yield but underneath while defining DV01, it says that DV01 gives the change in the value of security for one basis point decline in rates? Pls. clarify.

iii) In Hedge Ex. 1 of Chpt. 5, Tuckman in numerical example has not prefixed “-“ with $100 million whereas in the formula he has done so. Pls. clarify.

iv) Why risk neutral pricing works? I could not understand a single word of Tuckman.

Pls. clarify these.

Regards
Sipani

 

[David Harper CFA FRM]

Hi Sipani

i) This is about the difference between Par Yield and (Theoretical) Spot Rates. Must get this first, or the rest is difficult.

His 'Zero Coupon Bond' plot is the Theoretical Spot Rate (Term structure of spot rates) curve. This is maybe the (most intuitive) place to start: the zero coupon yield = spot rate on the single cash flow given by a zero-coupon bond.
For example, 3% spot rate for a 3-year Zero coupon bond:
Price = $100/(1.015^6)

The 'Par Yield' (if upward sloping theoretical spot) must be less: What is the coupon on a $100 bond that produces a price (PV) of $100? Must be < 3% (because we now have near term coupons to discount). This is hard to see: the par bond has coupons so it's yield must be less than 3%.

I will add an XLS on this....

ii) Yes, nice observation, it is the start of a bit of a confusing sequence and there are a couple of errors in the source Tuckman here (table 5.1 option prices are wrong).

This is correct: "DV01 [a.k.a., price value of a basis point] gives the change in the value of security for one basis point decline in rates" I advise, keep it simple here:

DV01/PV01 = $ dollar change in price/value given 1 basis point change.

Instrument can refer to a bond or an option. If option, DV01/PV01 equals option GREEK RHO.

Re: bonds,the key formula is DV01 = P*D/10,000

I advise you ignore the other Tuckman angle on this...you'll not on p 95 he introduces distinctions be we are concerned with the "simple" interpretation above

iii) The sign (-) is not critical. Technically, he could (should) have included in the example where it would signify to hedge the long (short) with a short (long) position. Sort of like we don't always include the (-) sign in VaR b/c we know what is meant

iv) Risk neutral is famously difficult. Can i point to this thread: http://forum.bionicturtle.com/viewthread/360/
And note link at end to 9-minute screencast on the risk neutral

Thanks,
David

append with correction: I meant option dv01= Greek rho/100