Question

4.[10 points] There are four bonds, A, B, C, D, with the following cash flows (dates in ycars, entries in $): Date 3 -134 10 30 150 B -0.8 1 -0.7 1 D -0.5 (a) (4pts) Construct an arbitrage in this market. (b) (1pt) To climinate the arbitrage opportunity, what should be the price for A? (c) (5pts) To eliminate the arbitrage opportunity, what should be the price for D?2

Answer 1

Oosters Goven data do meu mani “ -19 150 1010 ^) TO calculau embalage thgs marskog [for bona ^] By using above calcularons, we have 134 - CF/41+ V Tin) + C Fal (1+ vtanya + CF3/41+ Yton' -0 By SubS14119ng 911 values above equation 134 > 1501(1+ ytan) + 10 10 1+ ayran)? +30|( 14 yaanit where to By simplytying we get Youns 30.74 1. For bona B 0.7 = IC It ytan) y Tan = 19.52-1.

for mons 0.8 = || (Hvimo 1. VTD - 25.1, " Puy bond n and sell bond B and bond a M.) to calculas porce of By using equalis o, we get Price = 1501C1+19.52-1.) +101 C 14 19:52.1.) + 301 - Rond a pare a 150.07 0 0 catcclau (<ce of P For bond a Por bond a for bond c three year spot rate - 30-74-). too year spot rate - 19527.). two year spor sate - 25.1. .. (1+ ss) > (+53) XC 1+ 412,1)) where SB = three year spot rate 32 = two year apot rate &(2, 1) = one year fosward rate after too years $(2,3) = 50. 44.1,

By sub519tuting 4111 Values in abore equation, We ga: (1 + 30.974-1)= (1+19.52-1.) *(14 {(2,1)) :: $(2,1) - 56.44.. : porce of bondo 161456.44%) 0.64