Bond Arbitrage Example PDF

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Example:Arbitragewithbonds  BondAmaturesin2years,pays2%coupon,nominalis100,priceis94.478.BondBmatures in2years,pays3%coupon,nominalis100,priceis96.365.Computer1andr2.  Iftherearenoarbitrageopportunities,wecanapplythepricingequationtobondAandB:

 Solvingthesystem:r1=2%andr2=5% Supposeanewbond,C,isintroducedinthemarket.BondCisatwo‐yearzerocouponbond withnominalof100.Ifthebondstartstotradeat85,isthereanarbitrageopportunitynow? Wecanusethepricingequationtoverifyiftheno‐arbitragepricecoincideswiththetrading price: 𝐵 

100  90.7  85  𝐵  󰇛1  0.05 󰇜

 Thereisanarbitrageopportunity.ThearbitragestrategyconsistsofbuyingbondCandshort‐ sellingitsreplicatingportfolio.TofindthereplicatingportfolioforbondC,weformthesystem: 2𝑧  3𝑧  0 102𝑧  103𝑧  100 whichissolvedby𝑧  3, 𝑧   2. Thecostofthereplicatingportfoliois94.478𝑥3  96.35𝑥2  90.7,thatis,itsno‐arbitrage price.Thecash‐flowsofthestrategyareasfollows: 

 Long(buy)1xC ShortRP: *Short3xA *Long2xB  Total 

Cash‐Flows t=0 t=1 ‐85 0

t=2 100

 283.434 ‐192.73

‐6 6

‐306 206

5.704

0

0...