Accrued Interest & Dirty Price Calculation in Bond Pricing

[kayy]

Hi -

I have a question on the accrued interest calculation for a Bond.

Consider an example where I buy 1m bonds at $98 (with maturity 1-Jan-2020, rate = 10%, frequency = 1, YTM = 11%, PAR = 100) from ABC on 1 – August -2012.

Clean Price = $98, Coupon amount - $100,000, Last coupon date : 1-Jan-2012

Next Coupon Date : 1-Jan-2013, No of days the bond was held by ABC = 210

Accrued Interest = (210/360) * 100,000 = $ 58,333.33

fraction of the compounding period remaining between settlement date and next coupon date = 1-0.58333 = 0.41667

Settlement dirty price = CleanPrice + Accrued Interest = $98*100,000 + $ 58,333.33

I see the above formula is used by most of the pricing systems to find the accrued interest and dirty price but I am not able to understand why we take the undiscounted value of the accrued interest and not the PV of the accrued interest ?

$ 58,333.33 - Shouldn't this be the accrued interest at the next coupon payment date and Accrued Interest at settlement date = PV (of accrued interest at next coupon payment date) = 58,333 /(1.1)^0.41667

Appreciate anyone's help in answering my question.

Thank you in advance.

 

[Ken Abbott]

Garbade has the last word in this subject area.

 

[quotes]

That is because bond traders quote their prices by accrued interest+clean price. The calculation of accrued interest helps traders quickly filter out the effect of different interest payment days and compare clean prices between bonds. Of course the standard way should be comparing yield to maturity where compound interest rate is considered and clean price is unnecessary. However, the yield calculation which requires goal seeking is more complex than simple clean price calculation. That is why people would rather choose the not so accurate clean price valuation for its simplicity.

It gets so popular that traders only quote clean prices, and you have to add back accrued interest by youself in order to get back the original price (dirty price) to do any discount calculation.