Class 1B

Class 1 – Derivatives Notes

YTM – ROI anticipated / return made on the bond if it is held till maturity.

Assumption in the YTM calculation – Every coupon will be reinvested at the same interest rate.

Accrued Interest –

· From last payment of coupon till today, some days have passed. In case, I sell my bond now, I should get interest for this period. This is called accrued interest.

· Accrued interest is that which has been earned since the last coupon payment. Because the bond hasn't expired or the next payment is not yet due, the owner of the bond hasn't officially received the money. If he or she sells the bond, accrued interest is added to the sale price

YearFrac – A formula of excel denoting fraction of year.

If the interest rate falls on 31^st May of the month, then number of days for American is 31 and European is 30.

100 basis points = 1% = 0.01. Hence, 1 Basis Point = 0.0001

Duration (excluding convexity)–

Impact on the price of a bond for a given change in the Interest rate in market

= dp / dr (1st derivative or 1st level of sensitivity)

Where,

p = Price of Bond (Current)

R = YTM

Delta = Change in bond price wrt change in interest rate

For duration, Delta = (p) * (-D) * (δ r) / (1+ YTM/ m), where,

· m = number of compounding

· p = Price of Bond

· δ r = Change in Interest Rate

For modified duration, Delta = P * (-MD) * (δ r), where,

· Modified Duration, (-MD) = (-D) / (1+ YTM/ m)

For dollar duration, Delta = (-$D) * (δ r), where,

· Dollar Duration, (-$D) = P * (-MD)

Delta (including convexity)

(P) * (-D) * (δ r) / (1+ YTM/ m) ……………. It is called cushion (can be +ve or -ve)

+

(P) * (0.5) * (Convexity) * (δ r)^2 …………. It is always +ve (Better push)

Notional bond - The same is not trading in the market

Deliverable Bonds - For delivery, any bond with maturity not less than 6.5 years & more than 10 years becomes a deliverable bond. Mechanism must exist to equate bond to be delivered to the notinal bond being traded.

Bond Futures - It is a contractual obligation for the contract holder to purchase / sell a bond on a specified date at a predetermined price.

Price paid by buyer to seller = Settlement Price of Bond = Invoice Price

= Future Contract Price * Conversion factor of the bond that you deliver + Accrued Interest from last coupon date to date of delivery of the bond that you deliver.

Cheapest to Deliver - Always get delivered if I wait till maturity