Case study $2$ On $4$th June $2022,$ a trader delivers bonds to settle a short position in a June $202210-$Year US Treasury Note future.

The table below lists three deliverable bonds.

Redemption Date Annual Coupon Annual Yield Conversion Factor

$2/15/20300\mathrm{.}015000\mathrm{.}029310\mathrm{.}7314$

$2/15/20310\mathrm{.}011250\mathrm{.}029030\mathrm{.}6791$

$2/15/20320\mathrm{.}018750\mathrm{.}029140\mathrm{.}7046$

Additional information:

$$On $4$th June $2022$ the futures price was $140\mathrm{.}06$ quoted against a par value of $$100$

$$The futures contract size is $$100,000$

$$ Annual coupons for the three bonds are divided into two equal six$-$monthly instalments payable on $15$th February

and $15$th August each year

$$ At the start of the business day $4$th June $2021109$ days had passed since the last coupon payment with $72$ days

to the next coupon payment

Required a$)$Compute the accrued interest on $$100,000$ par value of each bond. $(5$ marks$)$

b$)$Estimate the invoice prices to deliver $$100,000$ par value of each bond. $(3$ marks$)$

c$)$ Estimate the dirty prices of the bonds and the total cost of $$100,000$ par of each bond $(12$ marks$)$

d$)$ Which bond is the cheapest to deliver and explain why the trader should prefer to deliver this bond. $(5$ marks$)$